You are here:
- Home
- Science
- Mathematics
- Number Theory
Number Theory/Questions Answered by Expert Vijilant
| Subject | Date Asked |
| Rates | 1/15/2012 |
| Q: I need the solution to have the form of (A X B X C)/( D X E) for the following. All cooks baking ... A: The amount of work that is done is the number of cook-hours. 4*6 cook hours are needed for 8 pies, ... | |
| Number Theory | 1/8/2012 |
| Q: I have the followingIs the following equation unique: A**n + B**m = C, where A, B,C, n and m are ... A: Once again, it will depend on the values of C and r. And also there will be multiple solutions if ... | |
| Number Theory | 1/6/2012 |
| Q: I have the followingIs the following equation unique: A**n + B**m = C, where A, B,C, n and m are ... A: Clearly this depends on the value of C. For example, if C = 2, we must have A = B = 1, but n and m ... | |
| Maths Application Example ? | 11/25/2011 |
| Q: The Above Attached Example of Children becomes which Maths application ? Multiplication Probability ... A: Once again it isn't a number theory question, but these are all permutations of male and female. Not ... | |
| number representation | 11/9/2011 |
| Q: i was wondering if there is any computer implementable method to determine the minimum number of ... A: Of course. It is very easy. Assuming you are thinking about positive integers, round up ... | |
| Olympics Games Medals. | 11/8/2011 |
| Q: http://en.wikipedia.org/wiki/Olympic_Games http://en.wikipedia.org/wiki/Olympic_medal ... A: This a rather tongue in cheek question, but I will answer it. First of all 3 is a very special ... | |
| Non-Integral Prime Numbers | 10/30/2011 |
| Q: Do Non-Integral Primes exist, and if so what are the example between 0 and 3pi? A: It depends on what number field you are working in. Clearly if you are in the integers, then you ... | |
| none | 10/28/2011 |
| Q: how many combination at 1 to 45 numbers A: You don't say how many you need to select from the 45. There would be 45C2 ways = 45*44/2 ways to ... | |
| Ratios | 10/13/2011 |
| Q: Can ratios have units? For example, if there are three combs and 5 pencils on a table, is the ratio ... A: A discrete variable is one which can take only a finite set of values. The most usual is whole ... | |
| Ratios | 10/13/2011 |
| Q: Can ratios have units? For example, if there are three combs and 5 pencils on a table, is the ratio ... A: I think that there is a great difference between discrete and continuous. The rates examples are ... | |
| nth root | 9/10/2011 |
| Q: plzzzz explain me the best method of finding nth root of a number.I studied nth root algorithm but ... A: . You haven't mentioned complex numbers. If that is what you mean you need to question me again. ... | |
| Number Theory | 9/10/2011 |
| Q: Sir, I had the following questions in my exercise, I failed to solve. Please look at these problems ... A: You only have to work out some terms and look for a pattern. It goes 0,1,4,13 = 2,7,22=0. So every ... | |
| Algebraic Square, Cube Formulas / Equations. | 9/10/2011 |
| Q: We have the following formulas 1. (a + b)^2 = a^2 + 2ab + b^2 2. (a − b)^2 = a^2 − 2ab ... A: Blaise Pascal investigated this while at school. Because he was so intelligent he got bored easily. ... | |
| Trignometric Equations | 9/8/2011 |
| Q: http://en.wikipedia.org/wiki/Trigonometric_functions Some Formulas ----------------- sin(A + B) = ... A: Once again you have asked me a question on a topic other than on number theory. But I can assure ... | |
| Quadratic Equation | 9/7/2011 |
| Q: http://en.wikipedia.org/wiki/Quadratic_equation As seen from the definition, a quadratic equation ... A: Q1 everywhere. For example finding the max or min values of a cubic expression. Take an A4 sheet ... | |
| Mathematics Quick Reference Guide or Maths Symbols Dictionary | 9/6/2011 |
| Q: Can we have a Maths Symbols Dictionary or Maths Symbols Quick Reference Guide similar to Oxford or ... A: Let's keep trying to save the planet! There is absolutely no need to cut down trees for paper to ... | |
| whole numbers and midpoints | 9/6/2011 |
| Q: Find three whole numbers such that the average of any pair is not a whole number. Find 5 points in ... A: Both of these are impossible. For 3 integers, there must be either at least two even or at least 2 ... | |
| Sets Operations Order of Computations | 9/5/2011 |
| Q: Sets Operations Order of Computations ---------------------------------------------- Example ... A: Just as multiplication takes precedence over addition, so intersection takes precedence over union, ... | |
| Decimal Points Number Raised Power to Decimal Points Number | 9/5/2011 |
| Q: Some examples of Power / Exponent / Index 2 ×2 ×2 = 23 = 8 1.12 = 1.1 × 1.1 = 1.21 0.53 = 0.5 × ... A: You won't let this go, will you. About 60 years ago I was taught how to work out powers of numbers ... | |
| Decimal Points Number Raised Power to Decimal Points Number | 9/4/2011 |
| Q: Some examples of Power / Exponent / Index 2 ×2 ×2 = 23 = 8 1.12 = 1.1 × 1.1 = 1.21 0.53 = 0.5 × ... A: Your notation is not correct. 2 to the power 3 is typed 2^3 = 8. 1.1^2 = 1.21 0.5^3 = 0.125 10^6 = ... | |
| Simultaneous Equations | 8/26/2011 |
| Q: Referring to Definition of Simultaneous equations ... A: Well I will answer this one although it is really linear algebra. You haven't said what a, b etc ... | |
| Computing Inverse of a Matrix Applications | 8/26/2011 |
| Q: Matrix -------- http://en.wikipedia.org/wiki/Matrix_%28mathematics%29 Matrices Applications ... A: Your questions are not on number theory, but I have answered them because I can see how keen you are ... | |
| Division by Zero | 8/25/2011 |
| Q: Basic Mathematical Operations 1. Addition : Any number added to zero will give us the Number ... A: 0/x = y. Then multiplying both sides by x gives xy = 0. So if x is not 0, then y is. If x = 0, we ... | |
| Division by Zero | 8/25/2011 |
| Q: Basic Mathematical Operations 1. Addition : Any number added to zero will give us the Number ... A: Mathematicians deal with the problem by using limits. Division by zero is not allowed, but we can ... | |
| Computing Factorial of a Number | 8/25/2011 |
| Q: Referring to the link for Factorial http://en.wikipedia.org/wiki/Factorial The formula for ... A: You will love the on-line encyclopaedia of integer sequences. I typed in factorial. This is the ... | |
| Computing Factorial of a Number | 8/24/2011 |
| Q: Referring to the link for Factorial http://en.wikipedia.org/wiki/Factorial The formula for ... A: I think the best reason comes from combinatorics. The formula for nCr is n!/(r!(n-r)!). Now nCn is ... | |
| 6 number combinations from 1 to 45 | 8/24/2011 |
| Q: Sir, can i know whether in excel or any programme for getting all the 6 digit combinations using 1 ... A: A very simple Basic programme would do that for you. For example For A = 1 to 45 For B = A+1 to 44 ... | |
| congruencies | 8/21/2011 |
| Q: Respected Sir, I am very thankful to your previous solution. I have understand the questions are in ... A: 1) is perfectly correct. Please ask what part you don't understand. 2) is incorrect. Since we are ... | |
| congruencies | 8/20/2011 |
| Q: Sir, I have seen in my graduate book the following questions. Can you explain please... 1)Prove ... A: There are lots of ways to prove this, but the whole question suggests this way. First, if m > q-1, ... | |
| Mathematical and Physical Constants | 8/17/2011 |
| Q: Referring to the Wikipedia Link for Mathematical Constants ... A: We are into deep waters here. However, a physical constant like the velocity of light in vacuo does ... | |
| rational numbers | 8/17/2011 |
| Q: can u please help me to solve it,question like this. "The product of any rational numbers is a ... A: As you know, a rational number is one of the form a/b, where a and b are integers. Then the product ... | |
| Locks | 8/13/2011 |
| Q: Note: This is not a homework. There are 1000 students in a school. And there're 1000 locks in the ... A: An interesting question. A lock will be changed whenever the student number is a factor of the lock ... | |
| Divide by 0 Workarounds | 8/12/2011 |
| Q: I am trying to make a formula for something, but it is possible for some values to cause a division ... A: Well, of course you can't divide by 0, and 0/0 is not defined. What can be defined though is a ... | |
| Reflective Character Series - (Exact Replica of the Character/Letter/Alphabet in Mirror) | 7/27/2011 |
| Q: As similar to Reflective Number Series. we can also note down the Reflective character series for ... A: This is not really my field of expertise, but it is quite interesting. Which words in the English ... | |
| Mirrored Numbers - (Exact Replica of the Number) - Optics & Real Life Use ? | 7/26/2011 |
| Q: What i observe by looking at the Numeric Whole Numbers(Integers) in Mirror (Glass) Object are the ... A: I really can't see any use for these, but that shouldn't stop you doing some research. For example, ... | |
| Zero | 7/22/2011 |
| Q: 1. When we divide any number by the same, we get 1. What for 0/0? 2. Is infinity really exist? ... A: You have only looked at one example. If you put x = 0 in the others, you get 0/0, but you don't get ... | |
| Zero | 7/21/2011 |
| Q: 1. When we divide any number by the same, we get 1. What for 0/0? 2. Is infinity really exist? ... A: 1. You can't divide by zero, but you can work out a limit of a fraction where numerator and ... | |
| Number Theory | 7/19/2011 |
| Q: Respected sir, I have seen in the text book, the solution form of a recurrence relation is A_n = ... A: I will use a slightly different notation. Starting with the 2nd order difference equation aA(n+2) + ... | |
| Rates | 7/16/2011 |
| Q: If 4 books cost $80.00, what is the cost for 8 books at the same price? If 4 books cost $80.00, ... A: I thought I had answered this question. To use simple proportion, we need two quantities which are ... | |
| Number Theory | 7/2/2011 |
| Q: Please see the following questions. I had an idea about mathematical induction. But these problems ... A: For a proof by induction you have to demonstrate that (1) the theorem is true for the smallest value ... | |
| Numbers | 6/29/2011 |
| Q: I am Vinay and studying UG course. I have seen this service by google and I hope, you will solve my ... A: 1.6k is obvious, 6k+1 gies (6k+1)(6k+2)(12k+3). The first two factors are consecutive integers so ... | |
| arithmetical function | 6/28/2011 |
| Q: Respected sir, An arithmetical function a is called completely multiplicative if a(1) = 1 and a(mn) ... A: An example of a completely multiplicative function would by a(n) = n^2 because a(mn) = (mn)^2 = ... | |
| Discrete Mathematics | 6/26/2011 |
| Q: I believe that Number theory is a part of discrete Mathematics. So, Please solve the following ... A: There is still a mistake in the typing. It should be 11^(n+2) etc. We just need to multiply the ... | |
| Discrete Mathematics | 6/26/2011 |
| Q: Respected sir. Please answer the following Dms questions. 1. Let a, b and c are integers, where a in ... A: 1. We can write b = pa, c = qa (p,q integral) Then bx + cy = pax + qay = a(px + qy) Quite simple ... | |
| Discrete Mathematics | 6/25/2011 |
| Q: I believe that Number theory is a part of discrete Mathematics. So, Please solve the following ... A: Q1. 11n+2 +122n + 1 = 133n + 3, so cannot be divisible by 133. It leaves remainder 3. Q2. Numbers ... | |
| Euclidean Algorithm | 6/9/2011 |
| Q: I am working through the problems in this number theory book and I'm getting stuck for most of them ... A: This question is about linear combinations of p,q. (p,q) divides any linear combination of p and q. ... | |
| Very Large Numbers | 5/16/2011 |
| Q: I recently saw a clip from Carl Sagan's "Cosmos" in which he attempted to describe how ... A: Here is a link to the largest prime number known. ... | |
| Unique solution | 5/15/2011 |
| Q: I tried all my best to answer the question in the attachment. Please help. Thanks Aba A: This is certainly not a number theory question. It is an analysis question. But, it is your lucky ... | |
| Which number is larger? | 5/7/2011 |
| Q: Which of these numbers is larger (10^80 - 1)! (Note that it's FACTORIAL) OR ... A: This is a test of your application of the Stirling approximation. There are various versions, but ... | |
| Perfect Numbers | 5/4/2011 |
| Q: I have been working on this problem for awhile with no success. Show that a number of the form ... A: Sorry for the delay in answering this. I've been very busy the last few days. Let us see if you ... | |
| digit | 4/22/2011 |
| Q: what is the last digit in the number 7^300?Is there a formula for this?plzzzzzzzz clearly explain. A: This question is about FLT. Fermat's Little Theorem. If p is prime,and a is prime to p, a^(p-1) = ... | |
| Grid Creation? | 4/15/2011 |
| Q: I have a practical problem that I believe is mathematically impossible to solve. But, being barely ... A: Perhaps you have thought there was a fourth rule, that someone must be working from home each day. ... | |
| Cyclic Groups | 3/27/2011 |
| Q: I have to prove these any way I want but do not know where to begin: 1) The group of units in Z/mZ ... A: 1) This is false. For example, in Z12, U12 = {1,5,7,11} and this is not cyclic. It is isomorphic ... | |
| Cyclic groups | 3/23/2011 |
| Q: I have to prove that if a group has two elements of order 2, then it cannot be cyclic. I do not ... A: First of all we may realise that if an element is order 2, it generates a subgroup of order 2. By ... | |
| abstract algebra congruence | 3/12/2011 |
| Q: Prove that ax ≡ b(modm) if and only if (a + pm)x ≡ b + qm(modm) I am confused.... I ... A: There is nothing really difficult in this. Remember that adding or subtracting multiples of m does ... | |
| even or odd function | 3/12/2011 |
| Q: Sir, Is f(x) =0 is what kind of function? As per me, f(x) = f(-x)= - f(x). So, I think it is even ... A: I think we must define it as an even function. If f(x) = 0, then f(x)*f(x) = f(x) = 0. But an odd ... | |
| Inequation | 3/11/2011 |
| Q: a,b and c are positive real numbers. Prove that {(1+a)(1+b)(1+c)}^7 > 7^7 a^4 b^4 c^4 ANSWER: Hello ... A: You didn't tell me that you needed an AM/GM proof. The problem with such proofs is that I am a ... | |
| Inequation | 3/10/2011 |
| Q: a,b and c are positive real numbers. Prove that {(1+a)(1+b)(1+c)}^7 > 7^7 a^4 b^4 c^4 ANSWER: Hello ... A: My most sincere apologies. Even an expert occasionally misuses a calculator. Here is a correct ... | |
| prime number | 3/10/2011 |
| Q: I am working in field of prime number.Is it possible to find out prime number by formula in fix ... A: I'm sure you know that there is no simple formula for finding prime numbers. However, to find all ... | |
| Number Theory- Showing the algorithm for computing kth root mod m works when gcd(b,m) > 1 | 3/4/2011 |
| Q: Many of us in number theory are working together to prove this problem: If m is a product of ... A: That certainly clarifies the problem. I can't provide a solution as yet, but can show you my ... | |
| Number Theory- Showing the algorithm for computing kth root mod m works when gcd(b,m) > 1 | 3/2/2011 |
| Q: Many of us in number theory are working together to prove this problem: If m is a product of ... A: I've asked you to email this question to me to provide more information. You haven't said anything ... | |
| number theory | 3/1/2011 |
| Q: Let p and q be prime with q=p+2 when p>3. Prove that p is congruent to 2 modulo 3. Also prove that ... A: We have 3 consecutive integers: p, p+1, p+2. So one must be divisible by 3. It cannot be p, (p>3) ... | |
| number puzzle | 2/24/2011 |
| Q: I am stuck with this question. Can you help me ? Three brothers inherit n gold pieces weighing 1, ... A: The total weight is n(n+1)/2, and this has to be divisible by 3, so n is congruent to 0 or 2 (mod ... | |
| sum of two irrational numbers | 2/11/2011 |
| Q: how do you prove that ep+πq is always irrational, where p,q are rational numbers, e is the base ... A: Suppose to the contrary. Then ep+πq = r where r is rational. Then we may write p = a/b, q = ... | |
| GCD proof | 2/8/2011 |
| Q: Prove that if d is a positive integer, d|a, and d|b, then (a,b)=d iff (a/d, b/d) =1. A: I think the easiest way to do this is to consider linear combinations. If d is the gcd of a and b, ... | |
| Complex nuber & enteger | 2/7/2011 |
| Q: I have tried all my best to do these questions. For example, for part d my solution was: 14= [1 + ... A: Well done for having a try. I am going to write root(-13) as r to save a lot of time. You have ... | |
| Number Theory | 2/4/2011 |
| Q: I have difficulties in the below two questions which seek for your kind assistance; a) Prove that ... A: There are lots of ways of proving the first one. Perhaps the easiest is to use that if integers x ... | |
| Congruum & aquare number | 2/3/2011 |
| Q: This part of the question I ask earlier. Thanks Aba A: Just look at the previous solution. Find the equation p^4 = q^4 + k^2. This was necessary to find a ... | |
| Congruum & pythagorean triple | 2/3/2011 |
| Q: How about this one? Thans for your generous support Aba A: I'm disappointed that you haven't showed me some progress on this problem. You know the usual ... | |
| Elliptic curve & Enteger | 2/3/2011 |
| Q: I have done some of it like x(x-2)(x+2)factors x (-2, 0,+2) & y(0) intercepts, and drawing two ... A: OK Aba I'll take it a bit slower. You know that for a max or min dy/dx = 0. Well we used that to ... | |
| Distinct Primes | 2/3/2011 |
| Q: Assume b=p1p2...pk where p1,p1,...pk are distinct primes. prove that if b/a^n for some positive ... A: Consider any one of the primes, p. Then a has this prime in its prime decomposition as p^q and a^n ... | |
| Elliptic curve & Enteger | 2/2/2011 |
| Q: I have done some of it like x(x-2)(x+2)factors x (-2, 0,+2) & y(0) intercepts, and drawing two ... A: Well, of course it isn't a circle. It looks more like a rugby ball between x = -2 and 0. Then there ... | |
| Points on circle & pythagorean triple | 2/2/2011 |
| Q: Can you help this one pleas? Thanks Aba A: Substituting, we have: (a/b)^2 + (c/d)^2 = 25. Multiplying by b^2*d^2 we get (ad)^2 + (bc)^2 = ... | |
| Integers on a Circle | 1/31/2011 |
| Q: Please I need your help. PS see the attached file Thanks Aba A: (a) Firstly, we have the points where the circle crosses the axes: (5,0), (0,5), (-5,0) and (0,-5). ... | |
| grouping | 1/22/2011 |
| Q: Here's my question Say you have a group of number 1-59.With these number you want to match then up ... A: Yes. This is is just the nCr choose function. In your case 59C5. Say '59 choose 5'. Most ... | |
| Algebra | 12/31/2010 |
| Q: A man has a physical balance and a stone of mass 40 kg . He divides the stone into four parts ... A: The method is to express the number in base 3 For example. 20 = 202 in base 3. 2*3^2 + 0*3 + 2*1. ... | |
| about Dirichlet's Approximation Theorem | 12/23/2010 |
| Q: Vijilant, I am a high school students in US, who is interested in Mathematics and doing some ... A: I think you have answered your own question. By not including 0 and 1 you have proved something ... | |
| Percent-Day Method | 12/11/2010 |
| Q: I read the following in a business mathematics book regarding the percent-day method fot calculating ... A: This does seem an unnecessary complication. Every schoolkid learns the formula I = PTR/100. Here R ... | |
| Number Theory | 12/5/2010 |
| Q: Please answer for me: 1) Let a be an integer greater than 1. Show that (a^m - 1, a^n - 1) = ... A: There is still a notation problem. gj+1 could be g(j) + 1 or g(j+1). Suggest you use brackets to ... | |
| Number Theory | 12/5/2010 |
| Q: Please answer for me: 1) Let a be an integer greater than 1. Show that (a^m - 1, a^n - 1) = ... A: By the factor theorem, a^m - 1 has factors of the form a^f - 1 for every value of f which is a ... | |
| nombre "π" | 12/2/2010 |
| Q: I am a teacher of math to the classes secondary I am a teacher of math to the classes secondary If ... A: It sounds like you teach in a French classroom, or you are French. π radians is the same ... | |
| math | 12/1/2010 |
| Q: when we use "π" =3.14 and what's unit for "π" A: π is only approximately 3.14 of course. It doesn't have any units. Amongst other things it is ... | |
| series of equations - linear programming story | 11/29/2010 |
| Q: how do i set these problems up in order to solve them? Question 1 the waputi indians make woven ... A: I got s = 1053 and 1/3, b = 295 and 5/7. I suspect there is a misprint in the question as theses ... | |
| series of equations - linear programming story | 11/28/2010 |
| Q: how do i set these problems up in order to solve them? Question 1 the waputi indians make woven ... A: This is a linear algebra problem rather than a number theory one. The equations are: 24b + 30r + ... | |
| Msc in Maths distance learning | 11/25/2010 |
| Q: I am Ravi from India. I did my B.Tech in Indian Institute of Technology(IIT) in Biotechnology ... A: Probably your best bet is to do an Open University MSc. But you would have to find out if your ... | |
| Number Theory | 11/20/2010 |
| Q: Sir, can you explain me how to find the roots of the congruence f(x)≡ 0 mod 189, if ... A: You work out the discriminant of the quadratic. I'm sure you learned at your mother's knee that it ... | |
| Division in Number theory proof | 11/13/2010 |
| Q: Note: This exercise will be graded out of 10 instead of the usual 5. Prove the following: For all a; ... A: I am always a bit wary about answering a question which is a graded assignment. I will leave the ... | |
| number theory ; congruences | 11/6/2010 |
| Q: 1)how to answer 2^20 congruence x (mod47) 2)let p be an odd prime and let n be an integer not ... A: 1) I presume you mean: calculate 2^20 (mod 47). This is perhaps easiest done by repeated squaring. ... | |
| number theory | 11/4/2010 |
| Q: Let p be a prime = 3 (mod 4). Show that if x^2 + y^2 = 0 (mod p), then p divides x and p divides y. ... A: we write x = hX, y = hY, then x^2 + y^2 = h^2(X^2 + Y^2). Perhaps you didn't notice the difference ... | |
| number theory follow up | 11/4/2010 |
| Q: Let p be a prime. an element a in (Z/pZ)* is called a cube if there exists b in (Z/pZ)* with b^3=a. ... A: Taking an example to make it a bit more concrete. p = 5. Then (mod 5) 1^3 = 1, 2^3 = 3, 3^3 = 2, ... | |
| congruences | 11/3/2010 |
| Q: Let p be prime. show that the congruence x^2 = a (mod p^2) has no solutions if x^2 = a (mod p) has ... A: The first part is very easy. x^2 = a (mod p) has no solutions means there is no x for which x^2 - a ... | |
| number theory | 11/3/2010 |
| Q: Let p be a prime = 3 (mod 4). Show that if x^2 + y^2 = 0 (mod p), then p divides x and p divides y. ... A: Let gcd(x,y) be h. Then x^2 + y^2 = h^2(X^2 + Y^2). Then either both X and Y are odd, or one is ... | |
| number theory | 11/3/2010 |
| Q: Let p by prime. Show that every prime divisor of 2^p - 1 > p A: This is false. When p = 2, 2^2 - 1 = 3, so divisible by 3 which is not greater than 2. I can prove ... | |
| number theory getting started | 11/1/2010 |
| Q: I was recently taking some programming lessons and we came through the so-called floating numbers, ... A: I don't think there are any really easy books on number theory. Probably the best are the OU ones ... | |
| Square numbers | 10/21/2010 |
| Q: I asked a question about squares, but the volunteer is on vacation. I don't understand his answer ... A: There is a general method for solving x^2 = z (mod a^n) The idea is to solve it for x^2 = z (mod ... | |
| Properties of Arcs | 10/20/2010 |
| Q: Sir , why equal arcs subtent equal angles at the centre inside a circle . Can you pleas prove this ... A: You know that many geometric shapes have rotational symmetry. For example, a regular pentagon has ... | |
| Changing from base 10 to a given base | 10/19/2010 |
| Q: Directions Step 1: Find the largest power of n that will divide into the base ten number. Step 2: ... A: Had any good breakfasts lately? I jest. OK, so we need to work out powers of 7. 7,49,343, 2401. The ... | |
| modulo arithmetic | 10/19/2010 |
| Q: Greetings Sir, I've been told floating point numbers(numbers with decimals) dont exist modulo p ... A: The notation 1/x (mod p) is not used in number theory. x^(-1) is used. The natural numbers prime to ... | |
| Properties of Arcs | 10/18/2010 |
| Q: Sir , why equal arcs subtent equal angles at the centre inside a circle . Can you pleas prove this ... A: 60 years ago I learned a Euclidean geometry proof of this theorem. You just draw the corresponding ... | |
| Number Theory | 10/10/2010 |
| Q: i am actually reviewing for our exam this week..i hope you can help me prove these two. i really am ... A: You need to consider odd and even n separately. If n is even, then 2^n factorises as difference of ... | |
| Number Theory | 10/5/2010 |
| Q: can you please help me understand how these problems are solved...actually, we already answered ... A: Not an easy one. First of all, if p = 2 = 3^2 (mod 7), so p is a possibility. Using LQR, (7/p) = ... | |
| Direct & Indirect Proportions | 10/4/2010 |
| Q: Recently, I sent to you this question and your reply follows: A man can walk from his house to the ... A: We are really into the realms of fantasy here. Remember that I used the term slowness as the ... | |
| Continued Fractions | 10/2/2010 |
| Q: Could you please tell me how to go about answering thisFind the real positive number x with periodic ... A: It is a long time since someone asked me about infinite continued fractions. The idea is to call the ... | |
| Number Theory | 10/2/2010 |
| Q: Sir,this problem really drives me crazy..i hope you can help me with this one.thanks a lot! A: You should know that the phi function is arithmetic. Check you understand what this means. So ... | |
| Direct & Indirect Proportions | 9/30/2010 |
| Q: How can this indirect proportion be changed to a direct proportion to determine the answer? A man ... A: You always ask some thought provoking questions, don't you? Yes, of course it can. We need to use ... | |
| gcd proof | 9/17/2010 |
| Q: assuming that gcd(a,b) = 1, prove that gcd(a+b, a^2+b^2) = 1 or 2. A: We use the Euclidean algorithm and a^2 + b^2 = (a+b)^2 -2ab. Then gcd(a+b, a^2+b^2) = gcd(a+b, ... | |
| nth term | 9/14/2010 |
| Q: what is the nth term of 2,4,8,16,32,64,128,256... i have found a solution that you can use when ... A: When there is a common difference, we call it an arithmetic progression. When there is a common ... | |
| number theory | 9/12/2010 |
| Q: if M, N € Z+, gcd (M, N) = 1 and MN is a perfect square, then M and N must be perfect squares. ... A: We just consider the prime factorisation of MN. The indices of each prime are even. We now ... | |
| Number Theory | 9/10/2010 |
| Q: Expert:Vijilant Answering your answers. I don't understand your statement that 3^2 is not ... A: We are talking about integer solutions here. 3^2 cannot be expressed as the sum of the squares of ... | |
| Number Theory | 9/9/2010 |
| Q: To Vijilant,Expert: I hope you find this more satisfactory. Maybe this is similar to Fermat's proof ... A: There seem to be a number of errors. The first is about any square being subdivided into any number ... | |
| Remainder Theorem | 9/6/2010 |
| Q: What will be the remainder when the number 111...........1(123 times) (it means 1 is repeated 123 ... A: This is not an easy question. I suspect it might be a challenge question, rather than an ordinary ... | |
| euler's formula | 9/2/2010 |
| Q: We all know its one of the most beautiful math formulas e^(ix)=cosx+isinx; I'm just wondering if I ... A: How refreshing to find someone being inventive and challenging. My gut reaction was to say ... | |
| first digit of number | 9/2/2010 |
| Q: Greetings Sir, Is there any algorithm to get the highest digit(digit multiplied by the highest ... A: Here is an algorithm that will work. Call the number x. Discard any decimal part. Put n = 0. ... | |
| Number theory | 8/27/2010 |
| Q: I am so proud to know this site and its contribution on Mathematics. I am Paul, working in school ... A: This second Question is not a number theory question, but it is interesting. First denote the roots ... | |
| Number theory | 8/26/2010 |
| Q: I am so proud to know this site and its contribution on Mathematics. I am Paul, working in school ... A: The first Q is solved using the Euclidan algorithm. From your notes I think you need a way of ... | |
| number theory | 8/10/2010 |
| Q: find 9 integers such that they form an arithmetic progression and the sum of square of each of them ... A: Let the middle integer be x. Then the others are x +/-d, x+/-2d, x+/-3d, x+/-4d. Squaring and ... | |
| number theory | 8/10/2010 |
| Q: prove that any positive integer n,there exist at least n consecutive integers such that each of them ... A: I've never seen this before, but will give an algorithm for doing it. A formal proof by induction ... | |
| number theory | 8/10/2010 |
| Q: if a>0,n>=2,then a^2 can be expressed as the sum of consecutive positive integer. A: There is something wrong here. What is n? You can easily check that the square of a power of 2 ... | |
| Number Theory | 8/7/2010 |
| Q: hope you could again help me with this... 1. Show that that the powers of 3(mod17) are 3, 9 , 10, ... A: I'm going to save time by not saying (mod 17) each time. presumably you had no difficulty producing ... | |
| Sequence and Series | 8/5/2010 |
| Q: The Common difference of an Arithmetic progression is 2 and the common ratio of a geometric ... A: This looks very much like a homework question but I will answer it. Presumably you know the formulae ... | |
| number theory maths | 7/13/2010 |
| Q: Q)if a and b are two real numbers, given b>a, which would be greater: a^b or b^a? A: Because this is a real number problem, it is not a number theory problem. It is very tricky indeed ... | |
| number theory | 7/13/2010 |
| Q: sir, i really hope that you can help me with these problems: a) Given integers a,b,c,d,m,n,u,v ... A: I could write a book on congruences, but I can't do that here. I'll just do a little explanation. ... | |
| number theory | 7/12/2010 |
| Q: sir, i really hope that you can help me with these problems: a) Given integers a,b,c,d,m,n,u,v ... A: Let f = gcd(m,n). Then since u and v are both integral linear combinations of m and n, they both ... | |
| Rational Numbers | 6/11/2010 |
| Q: Sir, I read in a book the method of expressing a non-terminating decimal in the form p/q where p ... A: You didn't give an example with a digit which does not recurr. It is more instructive with one ... | |
| Theory of number | 6/7/2010 |
| Q: If p is a prime and p|ab then p|a or p|b. Plz give proof this theorem. A: I think a proof by contradiction is the easiest here. Suppose to the contrary. Then p divides ... | |
| Future Value & Compound Interest | 5/24/2010 |
| Q: I am having some difficulty with the following calculation for future value for compound interest ... A: The quantity you have written down is the amount after 3 years. 1.030301. The amount after 2 years ... | |
| Number Theory | 5/24/2010 |
| Q: I have two problems that I simply am lost on. Please help me if you can. First, I know that an ... A: You haven't told me which algorithm for subtraction you are using. Approx 66 years ago I was taught ... | |
| Future Value & Compound Interest | 5/21/2010 |
| Q: I am having some difficulty with the following calculation for future value for compound interest ... A: You may have misunderstood what was intended by someone with less familiarity than you with math ... | |
| Problem Solving for Teachers | 5/21/2010 |
| Q: I am hoping that you can help me to understand this question. Thank you! If 10 is removed from the ... A: Closed means you can't get outside the set by using the defined operation. If 10 is removed, then ... | |
| number theory | 5/9/2010 |
| Q: 1)show that any number of the form 4^n can never be expressed as sum of squares of 2 positive ... A: I have given you an example of such a proof. It is useful to prove the non-existence of solutions. ... | |
| number theory | 5/8/2010 |
| Q: 1)show that any number of the form 4^n can never be expressed as sum of squares of 2 positive ... A: First of all, such a number cannot be the sum of two odd squares since that is of the form 4k + 2. ... | |
| statement | 5/4/2010 |
| Q: would the following statement stand true? a number is a rational number if it has repeating ... A: Yes, this statement is correct so long as we have an appropriate definition of repeating decimal. ... | |
| linear congruence | 5/2/2010 |
| Q: i need help in formulating the equation and solution to this problem... " a troop of 17 monkeys ... A: Unless there is something you have left out, the number of monkeys is not important. It is a rather ... | |
| primes | 4/25/2010 |
| Q: How can I check if this works if we assume a number that is composed of digits x1,x2,x3,y like 1234 ... A: The digit sum you have calculated gives you the remainder on dividing your original number by 9. If ... | |
| number theory | 4/24/2010 |
| Q: may i ask again, how will i prove this in this form... i do understand your first proof, but what i ... A: You seem a bit upset about nothing. Two days ago we had the anniversary of William Shakespeare who ... | |
| congruences | 4/22/2010 |
| Q: prove thm. 1.16 (transitive property) if 12 congruent 6 (mod2) is equivalent to 2 divides ... A: I'll do it more generally a = b (mod m) and b = c (mod m), then a = c (mod m) a = b (mod m) means ... | |
| LCM | 4/21/2010 |
| Q: for any integer a, prove that [ 9a+8 , 6a + 5] = 54a^2+93a+40 A: You will observe that we are asked to prove that the lcm is just the product of the numbers. That is ... | |
| number theory | 4/18/2010 |
| Q: show that there is no integer n, such that 4 divides n squared minus two... A: If n is odd, so too is n^2 and also n^2 - 2. 4 does not divide any odd number. If n is even, write ... | |
| linear congruence | 4/14/2010 |
| Q: Consider the congruence 4x=2010 mod m. For which m>1 does it have solutions? For those cases where ... A: The congruence ax = b (mod n) has solutions if and only if the gcd(a,n) divides b. For example, if m ... | |
| Number Theory | 4/6/2010 |
| Q: Find all solutions of the quadratic equation x2 + 12x + 40 = 0 mod 37 Hint: Complete the square. I ... A: After completing the square you get (x+6)^2 = 33 (mod 37) There are no shortcuts if you think there ... | |
| Quadratic Reciprocity | 4/6/2010 |
| Q: completly lost. Hope you can help. Thanks. It is currently unknown if either of the following two ... A: I hope this is not a homynym for Knock-out. I'll start you off and think about the next part, as I'm ... | |
| Perfect numbers & Quadratic Congruence | 4/5/2010 |
| Q: 1.Let n be +ve integer and p is a prime, and let m=[(3^(n)).p]. Also m is a perfect number. ... A: I am always pleased when a student asks for further explanation. It proves that he/she is thinking ... | |
| Perfect numbers & Quadratic Congruence | 4/3/2010 |
| Q: 1.Let n be +ve integer and p is a prime, and let m=[(3^(n)).p]. Also m is a perfect number. ... A: please note a correction. The function sigma is needed, not phi. This is a very contrived question. ... | |
| The Legendre Symbol | 3/30/2010 |
| Q: I'm clueless on these two questions and hoping you can help me out. Thanks! {1}Prove that there are ... A: Your hint should read: (-1/p) = (-1)^((p-1)/2) = {1, if p = 1 mod 4 and -1 if p = 3 mod 4. If there ... | |
| multiplicative | 3/29/2010 |
| Q: If m >= is a positive integer, let f(m) be the number of (incongruent mod m) solutions to x^2 = 1 ... A: We have to show that if m and n are coprime, and there are a solutions of x^2 = 1 (mod m), t_1, ... | |
| math | 3/25/2010 |
| Q: do you have any activities for primary students about number theory Thankyou, A: As you know I have been a math teacher, mainly in secondary education. But I have granddaughters in ... | |
| numberseries | 3/3/2010 |
| Q: 3, 15, 24, 25, 30, 32, 35, 44,in a number series of 5 numbers only,at a time and never using the ... A: This is just the number of ways of arranging 8 objects all different, but only choosing 5. It is ... | |
| Euler's Theorem | 2/22/2010 |
| Q: I'm totally lost on these two problem. I'm hoping you can lend me a hand. Thank you very much. ... A: Remember that if x = y (mod p) and x = y (mod q) then x = y (mod pq) for p,q coprime. The expression ... | |
| congruence | 2/21/2010 |
| Q: These are two questions I don't know how to start. I'm hoping you can hep me out. Thank you. ... A: a_2 = 7^7 = 43 (mod 100) We now need to calculate 7^43. This is where we use Euler's extension of ... | |
| Mathematical Reasoning | 2/19/2010 |
| Q: 1. If 63 books cost $126, what will 125 books cost? Calculation: ($126 X 125)/63 Explanation: If ... A: Yes, I think so. If only one man is available it will take him 15 times longer to do the work, so it ... | |
| Sum of squares of 2 integers question | 2/19/2010 |
| Q: Prove that if both x and y are coprime to 3, then x^2 + y^2 is not a perfect square. Thanks a lot. A: This is just a matter of working out the different possibilities (mod 3). Either both congruent to ... | |
| pythagorean triples | 2/16/2010 |
| Q: sir or madam, my name is john, down here in Texas. been going to grad school about the last two ... A: Think about what the other sqares could be. They must be both odd or both even. If both odd, ... | |
| real number | 2/9/2010 |
| Q: if 'a' and 'b' two real number if a > 0 then -a < 0 proof:- a > 0 a-a>0-a 0>-a if a < 0 then -a ... A: I presume you haven't any problem with subtracting a from each side of the equation. -a is greater ... | |
| modulo / congruence | 2/8/2010 |
| Q: [Question 1] Find, with proof, the smallest positive integer n that satisfy all the congruences. n = ... A: This looks hard, but is easy, because in each case, n = -1 (mod a) for each a. So we need to work ... | |
| Congruence question | 2/3/2010 |
| Q: Please look at the image attached. Thanks a lot. A: To prove that x(s) is in Z, expand by the binomial. The 1/a terms cancel, and all the rest are ... | |
| Mills & Property Taxes | 2/1/2010 |
| Q: I saw this calculation and I do not know how the mills unit cancel: Tax = Assessed value X (Mills ... A: I think I may have answered this question before. 20 mills per dollar = 20mill/dollar. Now 1 dollar ... | |
| pi | 1/30/2010 |
| Q: 1.Why pi is an irrational number, since pi=circumference/diameter(If both circumference and ... A: Every proof that PI is irrational is difficult and demands at least a very good understanding of ... | |
| number theory | 1/24/2010 |
| Q: prove that the sqrt of 13 is irrational A: Suppose to the contrary. root 13 is raional = a/b where a and b are integers with no factor in ... | |
| completness | 1/17/2010 |
| Q: you give great solution for my previous post and I am expecting the same too. A. What is order ... A: This is not an easy thing to do in a short answer. I think you mean that A is a subset of the reals. ... | |
| squaring and taking roots | 1/17/2010 |
| Q: Read this example before theAccording to pythagoras, hyp^2=adj^2+opp^2 Taking square root on both ... A: Geometry is one way to look at squaring and cubing. A fourth power may be thought of as the volume ... | |
| completness | 1/16/2010 |
| Q: you give great solution for my previous post and I am expecting the same too. A. What is order ... A: This is not really my expertise but I will try to answer it. As far as I understand it, an order ... | |
| squaring and taking roots | 1/16/2010 |
| Q: Read this example before theAccording to pythagoras, hyp^2=adj^2+opp^2 Taking square root on both ... A: This is a common mistake for math students. Fortunately, there is a clue in the notation. Squaring ... | |
| Rates | 1/14/2010 |
| Q: My previous question and your reply follow: How would I determine the answers to the following by ... A: My point was that the vast majority of the time was oven time, and this did not depend on the number ... | |
| numbers | 1/14/2010 |
| Q: Sir-Thanks in advance for math help. If A = {r belongs to Q such that r^2<2} and B = {r belongs to Q ... A: The continued fraction convergents for sqrt(2) are: 1/1, 3/2, 7/5, 17/12, 41/29, 99/70, ... | |
| combination | 1/7/2010 |
| Q: Our class of 16 people must elect a president, vice- president,secretary,and treasurer. Janet says ... A: I will assume that no person can hold more than one office. The President can be chosen in 14 ways, ... | |
| Derivative Fibonacci Sequence | 12/29/2009 |
| Q: I "googled" the numerical sequence 0,0,0,0,1,1,2,3,4,5,7,7,... and it was identified as Fibonacci, ... A: Your sequence certainly isn't Fibonacci. Google found Fibonacci because terms 4,5,6,7 and 8 are ... | |
| how do you find several primes in a small gap? | 12/21/2009 |
| Q: I am familiar with the twin prime conjecture as well as with the work of Goldstone and others but I ... A: What a wonderful name. I have had the pleasure of singing the bass part in Mendellsohn's oratorio ... | |
| number theorey for excercise | 12/19/2009 |
| Q: 1. For any positive integer n,find lcm(n,n+1) ... A: 1. Since gcd(n,n+1) = 1, lcm(n,n+1) = n(n+1) 2. This is false since 0 cannot be so expressed. 3. ... | |
| Number Theory | 12/13/2009 |
| Q: I have a several of questions. 1)Show that 21 has no primitive roots. 2)Find the 4 solutios to ... A: n has primitive roots if and only if it is 1,2,4,p^e or 2*p^e, where p is an odd prime. 21 is not of ... | |
| Number Theory | 12/10/2009 |
| Q: Determine K such that 2x^2+3x-K is congruent to 0(mod 5) is solvable. A: The discriminant of this equation must be a qr mod 5. The discriminant (b^2-4ac) = 9 + 8k = 3k - 1 ... | |
| Num. Theory | 12/9/2009 |
| Q: This is a correction of a question I asked earlier. Prove using mathematical induction: For n > or ... A: You know that the first step in a proof by induction is to choose n = 1 and check if it is true. n = ... | |
| A little help please? | 12/9/2009 |
| Q: I'm having some issues working out these two problems and I was hoping you could help me? 1) ... A: The least common multiple of n and n-1 is n(n-1) which is greater than 6n for n > 7. The second ... | |
| Number Theory | 12/8/2009 |
| Q: Prove that if: the gcd (a,b)=1, then (a+b,ab)=1 Thank you. A: Here is one way to answer the question. Suppose to the contrary. (a+b,ab) = h, where h>1. Then a+b = ... | |
| Prime Factorization | 12/7/2009 |
| Q: I need some help with a Number Theory question about Gaussian Integers. Im supposed to explain why ... A: There are some mistakes in your typing. The first should be (5+3r2)(5-3r2), where r2 stands for ... | |
| Number Theory | 12/6/2009 |
| Q: If p,q are distinct primes and a is any integer then a^pq-a^p is congruent to a^q-a(mod pq) A: Is you dad a mountain climber by any chance? It is still not known if George Mallory was the first ... | |
| need asap help | 11/22/2009 |
| Q: Hey I can't figure these out, do we have enough info? 1)A lighthouse is located on a small island 3 ... A: Call A the angle the beam makes with LP and x the distance of the beam on the shoreline from P. Then ... | |
| Question | 11/21/2009 |
| Q: Define the infinite sequence of natural numbers a(1)=2009 , a(2)=20092009 , ... A: a(2010) = 2009(1 + 10^4 + 10^8 + ...10^(4*2009) =2009(10^(4*2010) - 1)/9999 using rule for sum of a ... | |
| Number Theory - Mersenne Primes | 11/16/2009 |
| Q: In a chapter titled Mersenne Primes, a question is asked not of the Mersenne prime format, and I am ... A: This question is really about the factor theorem. Do you remember it? A polynomial p(x) has the ... | |
| ap calculus ab | 11/10/2009 |
| Q: my problems (set 2): In Exercise 19 find dy/dx. 19. y=(x+1)(x+2)/(x-1)(x-2) 20. Use the definition ... A: I hope these aren't homework problems. It's OK if you have managed to do 1 to 18 yourself. 19. You ... | |
| ap calculus ab | 11/8/2009 |
| Q: my problems (set 1): 2. What is the limit of (4-x˛)/(x˛-1) as x approaches ∞? (A) 1, (B) 0, ... A: These aren't problems but routine examples. I suspect you haven't studied worked examples of the ... | |
| ap calculus ab | 11/4/2009 |
| Q: my problems (set 2): For Exercises 9 and 10 find the derivative of each expression and simplify. 9. ... A: You don't say what to differentiate with respect to, but I shall assume it is x. 9. (1/a)(2x/b - ... | |
| urgent math | 11/3/2009 |
| Q: Hey there I have a test tomorrow nigh for Calc and I just can't seem to get the answers for these ... A: You have left it late. Why didn't you query days ago. It is past midnight here in the UK and ... | |
| trigonometry | 10/31/2009 |
| Q: Sir, please solve these problems soon, If cos2B=cos(A+C)/cos(A-C) then show that tanA,tanB and ... A: This is not my expertise, but I will help you with some of them. cos(2B) = 2 cos^2(B) - 1 = ... | |
| math | 10/27/2009 |
| Q: i dont get how you figure out how far away a term is from another example: 1,2,6 ,120, ,5040 A: Recognising a sequence is a matter of knowing the rules of basic sequences and trying to see if you ... | |
| Number Theory | 10/26/2009 |
| Q: if n>4 is a composite number, show that n|(n-1)! Conclude that (n-1)! is not congruent to -1(mod n). A: Unless n is a square, it can be factorised, and both of these factors are less than n, and can be ... | |
| Number Theory | 10/26/2009 |
| Q: I will use = to mean congruent. Using the fact that p-j = -j(mod p), show that if p is an odd ... A: Sometimes substituting in an answer you are asked to prove helps, so you were right to try that. ... | |
| Number theory | 10/21/2009 |
| Q: Sir, 1) How many pairs of non-negative integers (m,n) each sum to 1492 without any carries? 2) If ... A: 1) Call the two numbers A and B. They are not equal since that would involve carrying. Number A has ... | |
| Circles | 10/21/2009 |
| Q: I need ur help though my question is not from number theory but geometry I1, I2........ I2005 are ... A: You certainly ask some varied questions! The only geometry needed here is 'arc = rǾ.' So Ik has ... | |
| urgent math | 10/21/2009 |
| Q: I REALLY need to know how to go about finding the inverse of a transcendental function. I have no ... A: Don't worry over this. You aren't going to be asked to do something impossible. Trust me. Inverse ... | |
| Math | 10/19/2009 |
| Q: I just don't know where to start on these questions just some advanced questions that I didn't have ... A: The given information says |x-2| < δ, so multiply by 2 to get |2x-4| < 2δ. then δ = ... | |
| Number Theory | 10/19/2009 |
| Q: find for what values of n "phi(n) is odd". Thanks for your help ANSWER: Hello Skrosuri The only ... A: 1. It is easily proved that the φ(n) integers less than n and prime to it form a ... | |
| Compex Numbers | 10/18/2009 |
| Q: Can Sinus and Cosine work on complex numbers?(For instance can we have Cos(i)?) Many Thanks ... A: This is not really my expertise, but I'll answer it. Of course it is necessary to redefine sin and ... | |
| Number Theory | 10/16/2009 |
| Q: Prove that when n is odd and a is an integer that a^n = a(mod3), where '=' means congruent. My ... A: This is another that can be done using FLT. Let n = 2k + 1. Then a^2 = 1 (mod 3) if a is not a ... | |
| Number Theory | 10/16/2009 |
| Q: Show that for any integer, a, a^561 = a(mod 561), with '=' meaning congruent. My thoughts: Since ... A: A composite number n such as 561 with a^n = a (mod n) for all a is called a Carmichael number, and ... | |
| mobius inversion | 10/15/2009 |
| Q: let f be an arithmetic function and let g(n) = ∑ (over d|n) of μ(d)f(n/d) show that f(n) ... A: This is a standard theorem in the theory of arithmetic functions and the proof will be found in most ... | |
| math -sequencing-arithmetic/geometric | 10/14/2009 |
| Q: what is the missing term in the following sequence ___,1_____,______,125,______,... ... A: With the usual notation for an AP, a + d = 1 and a + 4d = 125 Subtracting gives 3d = 124 and d = 41 ... | |
| Riemann Hypothesis and Prime Numbers | 10/11/2009 |
| Q: Can you simplify and explain the Riemann Hypothesis up to a middle-school math level? A: The answer is a very firm NO. I have the book Prime Obsession by John Derbyshire, which I think is ... | |
| Number Theory | 10/11/2009 |
| Q: find for what values of n "phi(n) is odd". Thanks for your help ANSWER: Hello Skrosuri The only ... A: 1) This is just another way of stating the Chinese Remainder theorem. suppose (mi,mj) = h. Then mi ... | |
| Number Theory | 10/10/2009 |
| Q: find for what values of n "phi(n) is odd". Thanks for your help A: The only values of n for which phi(n) = 1 are 1 and 2. Suppose in the prime factorisation of n, a ... | |
| Circles | 10/8/2009 |
| Q: Given two concentric circle of radii r,R From a point P on the smaller circle, a straight line is ... A: This certainly isn't number theory, so I should reject it, but I'm pretty good at geometry, so I'll ... | |
| number theory | 10/2/2009 |
| Q: Q 1: A= (1999)^1999 B = sum of digits of A C = sum of digits of B D = sum of digits of C Find sum ... A: Q1 1999 = 1 (mod 9) So 1999^1999 = 1 mod 9. log(A) = 19998log(1999) = 6598.3.... This means A has ... | |
| math | 9/26/2009 |
| Q: This is question from absolute value properties Question |a|>= and |a|>=-a Proof: if a>=0 then ... A: I just think you need to look at a few examples, or look at a number line. a = 3. |a| = 3. -a = ... | |
| division | 9/26/2009 |
| Q: If we divide a number, is the answer always smaller? A: I presume we are talking about positive numbers here. Dividing a number by a number greater than 1 ... | |
| ap calculus preparation | 9/24/2009 |
| Q: 9. For question 9, find the standard equation of the circle satisfying the given conditions. A ... A: I should reject these questions since (a) These are not number theory questions, but coordinate ... | |
| Number Theory | 9/22/2009 |
| Q: I'll use = to mean congruent.... if a=b(mod n) and d|n, show a=b(mod d). I assume that I would ... A: An exam question might give you the clue; prove from the definition of congruence... So in this sort ... | |
| number theory | 9/21/2009 |
| Q: My questions are : a>How many triangular number ,less than 1000 ,can be expressed as the difference ... A: (a) The difference of squares of consecutive natural numbers is calculated as (a+1)^2 - a^2 = 2a + ... | |
| Number Theory - Congruences | 9/17/2009 |
| Q: I have 3 questions. 1) 1) Show that for infinitely many n, 43|(n^2 + n + 41). The answer will be ... A: We have to find solutions to the congruence equation: n^2 + n +41 = 0 mod 43 41 = -2 (mod 43) so (n ... | |
| number series | 9/1/2009 |
| Q: find out the missing number: 8,12,18,_____,40(1/2) A: I'll assume you mean 40.5 for the last term. In that case it is a geometric progression. You get ... | |
| 4th year university number theory question | 8/30/2009 |
| Q: I need to show that the gcd(lcm(a,b), lcm(b,c), lcm(c,d)) = lcm(gcd(a,b), gcd(b,c), gcd(c,d)) is ... A: No wonder you had difficulty proving it! It isn't correct. Take any prime p, and denote the index ... | |
| number theory proof | 8/27/2009 |
| Q: I need to show that the sum of the reciprocals 1+1/2+1/3+...+1/n is never an integer for n>1. I've ... A: I'm not going to set out the whole proof, but give you the idea of how to proceed. You can use ... | |
| number theory | 8/27/2009 |
| Q: I need help with the following problem. I can't figure out how to set it up. (Brahmagupta, 7th ... A: I didn't give the smallest solution first time. Here is the revised version. This is a fairly ... | |
| number theory2 | 8/22/2009 |
| Q: look the image please A: I'll answer your first question and think about your second. Every prime number of the form 4k + 1 ... | |
| math | 8/12/2009 |
| Q: Let a and b be two non zero rational numbers such that the equation ax*2+by*2=0has a non zero ... A: From the given equation, putting the solution x = c/d, y = e/f, c,d,e,f integral, we arrive at a = ... | |
| inequalities | 7/29/2009 |
| Q: if a,b,c,d>0 show that a/b + b/c + c/a >= 3 and a^2 + b^2 + c^2 >= 3.(a^2.b^2.c^2)^1/3 A: These are very easily proved by using the theorem that for a set of positive numbers, their ... | |
| Interest & Percentages | 7/28/2009 |
| Q: An investor wants to divide $1000.00 into two amounts, $800.00 and $200.00 for a total return of ... A: You are still an algebraphobe then. There isn't. If we do use algebra 200 at x% and 800 at y% we ... | |
| Math | 7/27/2009 |
| Q: composite integers n for n divides 2^(n)-2 are called pseudoprimes ,Show that every fermat's Number ... A: It's a good job there was a hint. I could have been hours working this one out without it. Fn = ... | |
| clarification | 7/27/2009 |
| Q: Your question is not clear, Does x3 stand for x^3 and x2 stand for x^2. Does 1/3x mean (1/3)x or ... A: After multiplying by 27, you get f(x) = 27x^3 + 27x^2 - 72x + 28 = 0. It is now a matter of using ... | |
| finitude of primes | 7/27/2009 |
| Q: Vijilant, How do I prove that there is not a finite number of primes of the form 4k + 3 and 4k - 3, ... A: These are theorems in most textbooks. I'll give you an outline, but you should find the proofs in a ... | |
| number theory - prime numbers/perfect numbers | 7/25/2009 |
| Q: Could you help me prove that if 2n-1 is prime, then 2p-1(2p – 1) is a perfect number? (Perfect ... A: A lovely name. It was my mother's. You seem to have a garbled version of the theorem. It should ... | |
| number theory | 7/24/2009 |
| Q: for any integer 'n' greater than 1,prove that (4^n+n^4)is never a prime. A: When n is even, the number is even. When n is odd and prime to 5, 4^n is congruent to -1 mod 5, and ... | |
| number theory | 7/22/2009 |
| Q: in 1886, a 16 year old italian boy announced that 1184 =2^5.37 and 1210=2.5.11^2 form an amicable ... A: This is question 10 of problems 10.2 of Burton's book. No answer is given. We need to show that ... | |
| number theory | 7/22/2009 |
| Q: prove that the Mersenne number M19 is prime hence the integer n=2^18(2^19-1)is perfect Hint:the only ... A: There is a theorem that says that the only divisors of M(p) where p is an odd prime have the form ... | |
| number theory | 7/22/2009 |
| Q: Verify: The product of two odd primes is never a perfect number? Hint: expand the inequality ... A: I think you can do this one for yourself. You know that sigma(pq) = sigma(p)*sigma(q) = (p-1)(q-1) ... | |
| number theory | 7/22/2009 |
| Q: Verify that: a) no power of a prime can be perfect number. b) A perfect square can't be a perfect ... A: I hope you are doing similar questions for yourself. I don't just want to do your homework for you. ... | |
| number theory | 7/22/2009 |
| Q: The Ciphertext message produced by the RSA algorithim with key(n,k)=(1643,223) is : 0833 0823 ... A: 1643 = 31*53, so we need the inverse of 223 (mod 30*52) 7*223 = 1561 = 30*52 + 1, so this checks ... | |
| Number theory | 7/21/2009 |
| Q: show that 3 is a quadratic residue of 23 , but a nonresidue of 31 A: You need to be familiar with the law of quadratic reciprocity to do this one. (p/q)*(q/p) (where ... | |
| prime-perfect square | 7/21/2009 |
| Q: I have two questions! No prime number can be a perfect square?Which of the following is not a ... A: The tower of Hanoi is certainly a math puzzle. Tetris and John Conway's Game of life are perhaps ... | |
| number theory | 7/21/2009 |
| Q: if every prime that divides n also divides m ,establish that Φ(nm)=n Φ(m), in patricular ... A: Let the prime divisors of m be p1,p2,p3,....pr. Then nm has the same set of prime divisors. Then ... | |
| number theory | 7/21/2009 |
| Q: prove that if the integern has r distinct odd prime factors, then 2^r divides Φ (n) A: Nothing is said about n having some power of 2 in its representation, but if it has the factor 2^k, ... | |
| nimber theory | 7/21/2009 |
| Q: verify that the equality Φ(n)= Φ(n+1)= Φ(n+2) holds when n=5186. where Φ is ... A: We need the prime factorisations of each number. Then we use the multiplicative property. ... | |
| number theory | 7/16/2009 |
| Q: if 'a'is prime to 'b'then (a+b)and (a^a-a^b+b^b)has no common factor other than '3'.-prove it. A: I think you may have mistyped this. I think the second number should be a^2 - ab + b^2. If this is ... | |
| Maths | 7/15/2009 |
| Q: Why does 0! = 1 ? A: It is a matter of definition. But a sensible one. It is clear that n! = n*(n-1)! for n > 1. The ... | |
| RE : Again on modular algebra problem | 7/6/2009 |
| Q: just to begin thanks a lot for your prompt answer for my past post. In fact maybe I explained the ... A: Sorry about the delay. I've had a busy marking load. If you can select the elements of S, it is ... | |
| pascal's triangle | 7/6/2009 |
| Q: I don't understand this.... Find a relationship between entries in Pascal's triangle and the maximum ... A: First we need to find a formula for the number of diagonals of an n-gon. nC2 =n(n-1)/2 gives the ... | |
| Possible ways of eliminating for a prime number | 6/11/2009 |
| Q: I am writing a JAVA program to find the next largest Mersenne's prime number. The standard way of ... A: This is an impossibly difficult question. On September 6th, the 46th known Mersenne prime, ... | |
| prime numbers and divisibility | 6/8/2009 |
| Q: Please help. I know that this may seem so elementary but these problems really have me stumped. ... A: The sum you require is 3+9+15+...999. That is, the odd multiples of 3. It is an arithmetic series ... | |
| logarithms | 6/3/2009 |
| Q: 1. If log_12(27)= a prove that log_6(16) = (4(3-a))/(3+a) 2. Let r = log_b(8/45) and s = ... A: Your tutor must be a sadist. These are the trickiest problems I have ever seen on logs. Perhaps ... | |
| hi sir pls help in this question | 5/31/2009 |
| Q: a number consist of two digits . the digits in tens place exceeds the digits in units place by 4. ... A: Take x as the units digit; then the ten's digit is x+4. The value of the number is then 10(x+4) + x ... | |
| Number Theory: Sums of 2 squares | 5/26/2009 |
| Q: Prove that if p is a prime number with p = 1 (mod 4) then p^2 = c^2+d^2 for some integers c and d ... A: First we need to prove or assume a theorem of Fermat which states that if p is a prime of the form ... | |
| Number puzzle | 5/18/2009 |
| Q: Using each of the numbers 1 to 9 exactly once to fill in the blanks and complete this equation: ... A: I don't normally answer number puzzles, but since my wife is Sheila, I'll make an exception. 12786 - ... | |
| squaring in base 6 | 5/12/2009 |
| Q: The question I have is after converting 95 to base 6, the answer is 235. How do I square 235 in ... A: The calculation is the sum of 9 multiplications. 200*200 = 40000 200*30 = 10000 (2*3) = 10 200*5 ... | |
| Multiple Investment Accounts | 5/11/2009 |
| Q: Some time ago I asked the following question and you determined the answer by using the solution ... A: You won't let this one go will you. Let's start with one of the solutions for the 3 account problem. ... | |
| number theory | 5/10/2009 |
| Q: How do I prove, If n^2 + m and n^2-m are perfect squares then m is divisible by 24? A: I can give a solution of this problem, but there may be a much simpler one. n^2 + m = a^2, n^2 - m = ... | |
| fibonacci - prove by induction | 5/7/2009 |
| Q: Prove f(fibonacci)4n is a multiple of three. My approach has been to make f4k+1=3k+3... But I am ... A: To do this you need to do a little investigation. Look at the pattern (mod 3) of the fibonacci ... | |
| proof by induction | 5/6/2009 |
| Q: not sure if you remember me but I am back :) We started learning proofs by induction. Could you ... A: I think you must be confusing the notation. <= is less than or equals. n! is never greater than ... | |
| congruences mod n | 5/5/2009 |
| Q: I need to know all the cases (for different mods), how do you find the residue of a large number ... A: Greetings Tom There are many methods available. In the case of a composite power the simplest is to ... | |
| proof by induction | 5/5/2009 |
| Q: not sure if you remember me but I am back :) We started learning proofs by induction. Could you ... A: 1. n = 1 LHS = 1^3 =1 RHS = 1^2*2*2/4 = 1, so theorem true for n = 1. Theorem true for n = k gives ... | |
| number theory, least common multiple | 4/29/2009 |
| Q: my ten year old is having a hard time understanding it can you help me explain for example 5,11, and ... A: You have to find the smallest number which is a multiple of each of the numbers. Start with 5 and ... | |
| discrete mathematics | 4/18/2009 |
| Q: I have been trying to solve a problem: prove or disprove: the sum of three irrational numbers is ... A: Given t irrational, to prove 3t is irrational. Suppose to the contrary, then 3t = a/b with a,b ... | |
| discrete mathematics | 4/18/2009 |
| Q: I have been trying to solve a problem: prove or disprove: the sum of three irrational numbers is ... A: This is the sort of question, that once you've seen the answer, you could kick yourself for not ... | |
| discrete mathematics | 4/17/2009 |
| Q: I have been trying to solve a problem: prove or disprove: the sum of three irrational numbers is ... A: Well done. You have done the hard part. The only thing that is not accurate is the initial ... | |
| discrete mathematics | 4/17/2009 |
| Q: I have been trying to solve a problem: prove or disprove: the sum of three irrational numbers is ... A: I'm not sure I understand the question. But to prove r3 is irrational is easy. Suppose to the ... | |
| discrete mathematics | 4/17/2009 |
| Q: I have been trying to solve a problem: prove or disprove: the sum of three irrational numbers is ... A: You are special because you have the same name as my mother born 1908. This is one you can disprove ... | |
| sequences | 4/15/2009 |
| Q: I'm trying to learn how to find the 7th term in the following sequence... -4,-6,-8,...,-2n,-2,... I ... A: You have the answer in front of you, but you have put an extra comma where there should not have ... | |
| Multiple Investment Accounts | 4/9/2009 |
| Q: Some time ago I asked the following question and you determined the answer by using the solution ... A: All the amounts must be positive. So 10,000 - 2t > 0, 20,000 -t > 0 and 3t > 0. From the first, 2t < ... | |
| number theory | 4/1/2009 |
| Q: Prove or disprove if (a^n) +1 is a prime number, than a is even and n is a prime number. also.. let ... A: For the first, we disprove by giving a counter-example. 1^1 + 1 = 2 is prime, but neither a =1 is ... | |
| probability and combinations | 4/1/2009 |
| Q: The “Pythagorean Triple Threat” is a co-ed softball team. The league they are participating in says ... A: Not too well actually. For the first part you have calculated the number of ways of permuting ... | |
| Number Theory | 3/30/2009 |
| Q: 1. Let a be any rational number that is not a perfect kth power. Show that the kth root of a is an ... A: I don't normally answer 4 different questions in one post. Today, you are lucky. I don't have ... | |
| permutation and combination | 3/28/2009 |
| Q: A train going from Delhi to Jaipur stops at seven intermediate stations.Five persons enter the train ... A: Perhaps that is the answer to a different question. There is no way the answer can be 10C2 - 10. ... | |
| permutation and combination | 3/26/2009 |
| Q: Suppose N different games are to be given to N children.In how many ways can this be done so that ... A: Unlike your previous question, this is a very easy one. Give all the children one game. This can be ... | |
| permutation and combination | 3/26/2009 |
| Q: A train going from Delhi to Jaipur stops at seven intermediate stations.Five persons enter the train ... A: I am assuming that we are only concerned with which tickets there are, and not with the order in ... | |
| permutation and combination | 3/26/2009 |
| Q: A die is rolled ten times.Find the number of ways so that the outcomesalways contain 1,2,3. A: I am assuming that by outcome you are only concerned with the count of each digit that ensues, not ... | |
| Number Theory | 3/19/2009 |
| Q: How do I solve: Show that if d|m then phi(d)|phi(m). Note: phi(m),phi(n) is Euler's phi function. ... A: With a question like this, a lot depends on which theorems you are allowed to assume. The obvious ... | |
| Congruences/methods of calculation | 3/19/2009 |
| Q: The question is: Show that 1^2, 2^2,...,m^2 is not a complete residue system modulo m if m > 2. ... A: Your question has now moved from fresher to graduate school. I did study pseudoprimes about 45 years ... | |
| pythagorean tripples | 3/18/2009 |
| Q: Doing a section on Pythagorean tripples, and I understand the simple examples, but these I just ... A: I'll show you a method for the first one which should enable you to do the second yourself. As with ... | |
| Mills & Decimals | 3/17/2009 |
| Q: I read the following in an old business mathematics textbook: "Express 13 mills as a decimal part ... A: frac() is just the same as decimal part of(). In other words you throw away the integer part of the ... | |
| Number Theory | 3/16/2009 |
| Q: find 13 consecutive composite positive integers...is there a formula for finding this? Prove that ... A: Consider 14! + 2, 14! + 3.....14! + 14. The first has factor 2, the second factor 3... the 14th ... | |
| Number Theory | 3/16/2009 |
| Q: Pn = P1P2P3….Pn +1 , where the Pi’s are the primes in increasing order of value. Prove that Pn is of ... A: We are concerned here about divisibility by 4 and 3. So we need to use the fact that P1 =2 and P2 = ... | |
| Mills & Decimals | 3/15/2009 |
| Q: I read the following in an old business mathematics textbook: "Express 13 mills as a decimal part ... A: You must be researching the history of maths teaching. The decimal part of a number is the part of ... | |
| recursion problem | 3/3/2009 |
| Q: a1=3, ak+1=ak-2 what is the value of the 4th term 1 is below a, k+1 is below a, and k is below a A: I was at the gym on the treadmill this morning, and sometimes that is when I have my best thoughts. ... | |
| number theory | 3/3/2009 |
| Q: (a U c) U (b U c) how to distribute and what is the answer I believe you get, a U b U c U A: First of all consider a Venn diagram. Three intersecting sets. The union of two sets can be ... | |
| additive/multiplicative inverse | 3/2/2009 |
| Q: When does a have an additive inverse (mod m), when does a have a multiplicative inverse and how ... A: a always have an additive inverse (mod m). It is -a, or m-a if you need a positive residue. a has a ... | |
| (A xor B)+ (B xor C)+ (C xor A)=(A xor B)+ (B xor C) | 2/18/2009 |
| Q: How can I prove that (A xor B)+ (B xor C)+ (C xor A)=(A xor B)+ (B xor C) using algebraic ... A: This is not quite my field of expertise, but I used to teach computer science, so I can answer the ... | |
| polynomial congruences | 2/6/2009 |
| Q: This problem is really throwing me off, I keep playing around with it, but I'm obviously not doing ... A: An interesting one which I haven't seen before. First of all (p-1)! = -1 (mod p) by Wilson's ... | |
| Congruences | 2/4/2009 |
| Q: The question is: Show that 1^2, 2^2,...,m^2 is not a complete residue system modulo m if m > 2. ... A: Let me answer your second question first. When we are asked to disprove something as in this case, ... | |
| binomials | 1/31/2009 |
| Q: What is the binomial series for (a + x)^63 thanks A: Not even mathcad can display all 64 terms of this expansion, but I can give you the first few terms, ... | |
| Fermat's Last Theorem | 1/29/2009 |
| Q: Find all integer solutions for a, b, c not congruent to 0 mod 5 for a^3+b^3=C^3 mod 5. I don't know ... A: I don't know how long this has been in the question pool. I don't usually look there. The question ... | |
| euler phi function. | 1/28/2009 |
| Q: There are two parts, prove phi(2n)=phi(n) and prove phi(2n)=2phi(n). Is the best way to solve this ... A: The first case is when n is odd, so that the factor (1 - 1/2) does not occur in the calculation of ... | |
| Simple Interest & Multiple Accounts | 1/27/2009 |
| Q: Some time ago I asked the following question and you determined the answer by using the solution ... A: It's because you can't have a negative amount of cash in an investment account. Unless you know ... | |
| Simple Interest & Multiple Accounts | 1/26/2009 |
| Q: Some time ago I asked the following question and you determined the answer by using the solution ... A: Yes there are lots of answers, only limited by the fact that you would want to have the number of ... | |
| Simple Interest & Multiple Accounts | 1/24/2009 |
| Q: Some time ago I asked the following question and you determined the answer by using the solution ... A: You already have a solution. 10,000 in the 2%, 0 in the 3% and 20,000 in the 5%. To put some in the ... | |
| number theory | 1/22/2009 |
| Q: I have two number theory questions. First, show that 561 is a pseudoprime, where 561=3(11)(17). ... A: I'll start with the second because that is much easier. The FLT assures us that a^(p-1) = 1 mod p ... | |
| Calendar Weeks & Days | 1/19/2009 |
| Q: If someone is paid every two weeks, he receives 26 paychecks per year, (52 weeks/year)divided by (2 ... A: Your original assumption that there are 26 paydays in a year is false. If payday is a Friday and ... | |
| Number theory/divisibility | 1/18/2009 |
| Q: My main question is this, since I'm a bit rusty: Let s and g>0 be given integers. Prove that ... A: First if and only if. Propostion A if and only if Proposition B To prove this we have to prove A ... | |
| proof | 1/17/2009 |
| Q: I have to prove by Contradiction the following If x,y are real numbers such that x + y is ... A: The idea of a proof by contradiction is to start by supposing the opposite of what we have to prove ... | |
| Set theory | 1/8/2009 |
| Q: simplify, showing your working out A n (A U B) ANSWER: Hello Mohammed We use the distributive law ... A: I make a rule not to answer more than 3 questions in one post. That is because i believe the student ... | |
| absoulte value | 12/28/2008 |
| Q: |a|≥a and |a|≥a Proof if a≥0 then |a|=a If a<0 then |a|=-a>a aєR ... A: An example |3| = 3, so |3| >= 3 |-5| = -(-5) = 5, so |-5| > -5 I think maybe you thought -a ... | |
| maths ask a question | 12/18/2008 |
| Q: is there any formula to find the sum of squares of the terms of an arithamatic progression ? A: Amazingly, I have never seen this question before, but it should be easy enough. S(n) = a^2 + ... | |
| Number Theory | 12/5/2008 |
| Q: I have 3 questions. 1) Given a is an element of Z, Prove: If a is even, then a^2=0(mod4) and if a ... A: 1) If a is even, the we can write a = 2b. Then a^2 = 4b^2 = 0 mod 4. If a is odd, we can write a = ... | |
| Permutations and Number Combinations | 12/3/2008 |
| Q: Using your example 4 placeholders out of 20 places and getting the answer 4845 number combniations, ... A: I'm not sure I understand what you mean here. Suppose we represent the 20 objects by the first 20 ... | |
| number theory | 12/3/2008 |
| Q: prove the converse of Wilson's theorem A: The converse is. If (n-1)! = -1 mod n, then n is prime. If n is not a prime, then it has a divisor, ... | |
| Mersenne primes and perfect numbers | 12/2/2008 |
| Q: A) show that a power of 3 can never be a perfect number B)more generally, if p is an odd prime, show ... A: First of all, your formula is not correct, it has an incorrect sign. A) Suppose it can, ... | |
| Number theory | 12/1/2008 |
| Q: If a^n+1 is a prime for some numbers a greater than or equal to 2 and n greater than or equal to 1, ... A: I don't think your statement a^n+1=a^m2^p+1=a^2pm+1=b^m+1 is correct. It doesn't include any ... | |
| Follow up question | 11/18/2008 |
| Q: I just had a few follow up questions about a question that you previously answered. Here is the ... A: x^2 + 5x + 1 = 0 mod 47 5 is even so add 47 to get x^2 + 52x + 1 = 0 mod 47 Now you can complete the ... | |
| Number Theory | 11/18/2008 |
| Q: Find the number of solutions to the congruence equation x^2+5x+1 ≡ 0 mod 177425. Note that ... A: I think this is a copy of the answer you need Questioner: Jules Category: Number Theory Private: ... | |
| mathmatics-number theory | 11/17/2008 |
| Q: determine those odd primes t for which -3 is a quadratic residue and those for which it is a non ... A: I assume that you can use the quadratic residues theorem. Firstly 2 is a a special case. -3 = 1 mod ... | |
| recurring decimals | 11/16/2008 |
| Q: quite often, but not always, the digits that form a recurring decimal occur in complimentary halves: ... A: This is a very interesting question, and I hadn't realised that before, so thank you. I will try to ... | |
| heavyweight | 11/14/2008 |
| Q: i am wondering if you could answer this for me.how much in, simplified form,is this:1e+60.like how ... A: I wonder if you are the Rodney from 'All fools and horses'. Or should it be elephants? 1E60 is 1 ... | |
| number theory | 11/12/2008 |
| Q: 1. Prove that ∛5 is irrational. 2. For any numbers a, b, (a, b)ⁿ = aⁿ ... A: I don't normally answer such a lot of questions in one post. Please don't ask more than 3 in any ... | |
| Series - Arithmetic or Geometric? | 11/11/2008 |
| Q: We know that the two following series is arithmetic and d=2. 2, 4, 6, 8, 10 3, 5, 7, 9, 11. ... A: A series in which each term is the reciprocal of the corresponding term in an arithmetic series is ... | |
| Modular arithmetic | 11/4/2008 |
| Q: How do I determine the last 2 digits of 3^400 using mod 100? ANSWER: Hello olebile phi(100) = ... A: I thought you might have been able to do #1 if you studied the previous answer, because we use the ... | |
| hard math problem | 11/3/2008 |
| Q: Find, with proof, the largest positive integer k with the following property: There exists a ... A: I don't know that there is a largest one. But let us take an example that works, and see why. ... | |
| Number Theory | 11/3/2008 |
| Q: What is the last 2 digits of 123^456? A: First of all, we need 123^456 mod 100. We use Euler's generalisation of Fermat's little theorem. ... | |
| Fractions | 11/1/2008 |
| Q: Example 1. 2/3 of Mary's age and 3/4 of Ruth's age equal Sarah's age. If the total ages equal 46, ... A: I'm sorry to disappoint you, but your method does not give the correct answer in the example. 2/3 of ... | |
| modular proof | 9/29/2008 |
| Q: i am having a real difficulty in proving this statement by induction. == is congruent symbol d> or ... A: This could be proved directly using the binomial theorem, but if you need a proof by induction here ... | |
| Number theory Proof | 9/26/2008 |
| Q: Let m and k be positive integers. Then the number of positive integers less than or equal to m*k ... A: My most sincere apologies for my horrendous mistake. I've answered so many questions successfully ... | |
| a counting and enumeration problem | 9/24/2008 |
| Q: I have a question that maybe I could have answered when I was taking probability 19 years ago but am ... A: This is an interesting problem I can help you with. Let us look at an example. How many selections ... | |
| Number theory Proof | 9/24/2008 |
| Q: Let m and k be positive integers. Then the number of positive integers less than or equal to m*k ... A: This is not true as stated. A counter-example is m=6, k=4. phi(6) = 4 so that k*phi(m) = 4*4 = 16. ... | |
| Odd and Even Multiples | 9/21/2008 |
| Q: I must find out how many multiples of 3 there are from 1-2008, then state how many and odd and even. ... A: This sounds like some Maths coursework where you have to put some graft in. Carefully list your ... | |
| how to find the primes in just a few seconds | 9/19/2008 |
| Q: i just want to ask how to find the 3 largest primes of 555,555,555,555.I know it's 37, 9901 and 101. A: Your number certainly has the factor 555. It is 555*(10^9+10^6+10^3+1) = 5*3*37*(10^6+1)(10^3+1) ... | |
| Number Theory | 9/18/2008 |
| Q: I'm so confused, I have no idea how to solve these... can you answer them for me? It would be a ... A: 1) You need to use the Euclidean algorithm property. (a,b) = (a, b-ka) or (a, ka-b). here we use a = ... | |
| Number Theory | 9/17/2008 |
| Q: I am new to this class and have never taken a proof class. I dont even know where to start on these. ... A: I'm not going to do all of these for you. They can all be proved by using the unique prime ... | |
| maths | 9/14/2008 |
| Q: if A equals 1 and Z equals 26 what word when times adds up to 1 million A: I can only help you with the maths of this question. After that it is up to try different ... | |
| terms and sequence | 9/13/2008 |
| Q: My daughter has a homework on terms and sequence with no real explanation of how or what they mean. ... A: A sequence is simply an ordered set of numbers, usually without end. e.g. 1,3,5,7,9,..... ... | |
| Explain" Every number can be written as difference of two squares" | 8/18/2008 |
| Q: "Every number can be written as difference of two squares" For example 24=7^2-5^2, 32= ... A: Welcome to my answer service. The difference of two squares is factorisable. x^2 - y^2 = (x+y)(x-y) ... | |
| number theory | 8/17/2008 |
| Q: 1.solve 6x+10y+15z=1 find x and y,z 2.if(a,4)=2,(b,4)=2,then prove that(a+b,4)=4; exibit three ... A: 4y+3z =1 mod 6 multiply by 2 8y + 6z = 2 mod 6 8y = 2 mod 6 1. Suppose there are only a finite ... | |
| number theory | 8/16/2008 |
| Q: 1.solve 6x+10y+15z=1 find x and y,z 2.if(a,4)=2,(b,4)=2,then prove that(a+b,4)=4; exibit three ... A: You are asking a lot of questions. I hope you are trying to solve them yourself before you ask me. ... | |
| number theory | 8/15/2008 |
| Q: 1.for every positive integer k show that (5^2)^k congruent to 1+3*2^(k+2) 2.let Fn=((2^2)^n)+1 Nth ... A: 1. You asked this earlier and I said it was impossible to answer, as you haven't specified a ... | |
| number theory | 8/15/2008 |
| Q: 1.prove that product of k consiquetive intigers is divisable by k1! 2.for every positive integer k ... A: 1. Let the largest of the integers be n. Then nCk, the number of ways to choose k objects from n is ... | |
| number theory | 8/11/2008 |
| Q: 1.find last two digits of 2^1000 2.(a,a+k)/k for a,knot equel to 0 3.(a,b)=1 and c>0 prove that an ... A: 1. 2^10 = 1024 =24 mod 1000 2^20 = 24^2 = 576 = 76 = -24 mod 1000 2^30 = -576 = 24 mod 100 Odd ... | |
| prime | 8/10/2008 |
| Q: Find all prime numbers(p,q,r) , that numbers pq+pr+rq and p^3+q^3+r^3-2pqr are divided by p+q+r. A: I'm afraid I don't have the time at present to do justice to this problem, but I would not be ... | |
| number theory | 8/10/2008 |
| Q: 1.find the no of solutions of x^2congruent x mod m and for all positive integers of m 2.pi(m)=pi(mn) ... A: 1. x(x-1) congruent to 0 mod m for every m, can only have the solutions x=0 and x=1. 2. I'm ... | |
| Watts & Watt-Hours | 8/8/2008 |
| Q: Can you explain the difference between watt-hours per hour and watts per hour? I thank you for any ... A: Suppose we take the example of a 1 watt indicator lamp. It is using energy at the rate of 1 joule ... | |
| combos | 8/6/2008 |
| Q: using 0-9 how many combinations are possible in a 9 digit combination A: Let's put it into a real situation. You are the manager of a team which plays 9 a side martian ... | |
| find the remainder when 7^51 is divided by 144 | 8/4/2008 |
| Q: find the remainder when 7^51 is divided by 144 A: We can use Euler's generalisation of Fermat's little theorem: a^phi(n) = 1 mod n if a is prime to n ... | |
| (a,p)=1,(n,p-1)=1 then x^n congruent a mod p has exactly one solution | 8/2/2008 |
| Q: (a,p)=1,(n,p-1)=1 then x^n congruent a mod p has exactly one solution A: I will have to assume that you mean p is prime. The p-1 numbers, 1,2,...p-1 form a multiplicative ... | |
| number theory | 8/1/2008 |
| Q: 1.x^3+4x+8 congruent to 0 mod 15 using chinese remainder theorem 2.how to solve 15x+12y+30z=24 A: We need to solve x^3 + 4x +8 = 0 mod 3 and also mod 5. The first is true for x=2 mod 3. The second ... | |
| math | 7/29/2008 |
| Q: how many 6 digit combinations can you make from 17 to 47 EX- 17 19 20 22 33 47? and can you send me ... A: This is 31C6 as there are 31 to choose from and we need to choose 6. Most scientific calculators ... | |
| plz enlighten me. | 7/25/2008 |
| Q: what about well ordering property,is there any proof in this? A: I think I said that the well ordering property is exactly that, a property and is part of the ... | |
| Probability | 7/24/2008 |
| Q: What is the probability of (a) two randomly chosen sides and (b) two randomly angles being equal in ... A: There is a subtle difference here, as the consecutive property is now given. Since every pair of ... | |
| Probability | 7/24/2008 |
| Q: What is the probability of (a) two randomly chosen sides and (b) two randomly angles being equal in ... A: (a) There are 3 different ways to choose the sides of the triangle, and only one is the equal sides, ... | |
| im bothered! | 7/21/2008 |
| Q: how to prove well ordering principle? A: I don't think this is something you can prove. It is one of the properties of the set of natural ... | |
| odd numbered fractions that dont equal 1 | 7/13/2008 |
| Q: I was just running through some numbers and wondering how almost all odd numbered fractions don't ... A: Your calculator can't show a recurring decimal. 1/3 is 0.3 recurring. A reasonably modern ... | |
| Number Theory | 7/11/2008 |
| Q: What is the formula to factor the binomial: 2^ab + 1 OR the binomial 2^ab - 1 (where a and b are ... A: If ab is a power of 2 there is no algebraic factorisation for 2^(ab) + 1 in real numbers. But we ... | |
| number puzzle | 6/25/2008 |
| Q: Can you answer this: work out the logic of these numbers and state which other number completes the ... A: Something tells me that this is not really a maths problem. Your sequence can be written 1*19, 2*12, ... | |
| number theory | 6/3/2008 |
| Q: I'm having trouble with this problem it's my first class in number theory so I don't have much of a ... A: Proofs in number theory are notoriously difficult, but don't despair. As you progress it gets ... | |
| math | 6/2/2008 |
| Q: The width of a rectangle is half as long as the length.The rectangle has an area of 128 square ... A: We need to use some algebra and denote the width of the rectangle by w feet. Then the length of the ... | |
| Can the following problem be solved using the Euclidean Algorithm? | 5/15/2008 |
| Q: This is a follow-up to my subject question about the local village gala The problem was solved for ... A: This has already been done. Here is a copy of my previous answer. We have two equations using pence. ... | |
| 6-digit combination | 5/5/2008 |
| Q: How can I get every possible 6-number combinations using numbers 0 to 49 on an excel spreadsheet? A: With great difficulty. You would need about 84 million cells. You could use a simple basic program ... | |
| Last question in my sons homework. | 5/1/2008 |
| Q: My sons homework is number sequences. example 7n-3 = 4, 11, 18, 25 etc. I understand how this works. ... A: Sorry for the delay. I didn't get the email. My ISP is sometimes too careful about eliminating ... | |
| proof | 4/27/2008 |
| Q: how can i prove that the number 1/square root of 2 is not a rational? how can i prove square of 2 is ... A: Sorry for the delay. I didn't get the email. My ISP is sometimes too careful about eliminating ... | |
| Euclidean Algorithm | 4/27/2008 |
| Q: Can the following problem be solved using the Euclidean Algorithm? At a local village gala, the ... A: Sorry for the delay. I didn't get the email. My ISP is sometimes too careful about eliminating ... | |
| Finding the nth term with no constant increase | 4/10/2008 |
| Q: I am stuck on finding nth terms when there doesn't appear to be a constant increase or decrease. is ... A: Sequences where there is a constant difference are called arithmetic sequences. Sequences where ... | |
| Congruences | 4/7/2008 |
| Q: Prove that 111^333 + 333^111 is divisible by 7 A: We will look at each term separately. 111 = -1 mod 7 and -1 to an odd power is -1 333 = 4 mod 7 By ... | |
| CRT | 4/5/2008 |
| Q: Sorry for the disturbance and I have the following confusion. Please clarify with suitable example. ... A: When we say there is one solution to a modulus equation, we mean that all the solutions are ... | |
| Recurrene Relations | 4/4/2008 |
| Q: I know something and I'm looking for a proof of it. Consider this recurrence relation. ... A: You could show that the second order equation you have quoted does satisfy the recurrence relation ... | |
| CRT | 4/2/2008 |
| Q: Sorry for the disturbance and I have the following confusion. Please clarify with suitable example. ... A: It all depends. If you have studied linear algebra, you will know that simultaneous equations can ... | |
| divisbility | 4/2/2008 |
| Q: Please show me how to prove: if a|c and b|c and (a,b)=1, then ab|c. Thank for your help. A: Probably the easiest way to see this is to consider the unique prime factorisation of a and b. The ... | |
| Repeating Decimals | 3/29/2008 |
| Q: Can you think of another calculation, one that is more simple, that can determine the fraction for a ... A: When I was at primary school over 60 years ago, we just learned the rule to put the recurring digits ... | |
| congurance | 3/25/2008 |
| Q: please see the following and give me a reply. generalize: Let a, b and c are some integers and c > ... A: You already know that you don't change the value of a mod b by adding a multiple of b. But cb is a ... | |
| comgurances | 3/24/2008 |
| Q: I am mahima and I came with the following two question after long gap. Please help me and give ... A: The first one is just saying that adding or subtrac any multiple of b does not change the value of a ... | |
| ZETA(4) | 3/12/2008 |
| Q: Is there any proof that shows us: ZETA(4)=pi^4/90 I can prove that ZETA(2)=pi^2/6 but for ZETA(4), ... A: You need to know how to calculate Fourier series. Define the function f(x) = -x for -PI<=x<0 and ... | |
| in regaurds to your contropositive proof on 9/10/2007 | 3/7/2008 |
| Q: I understand the basis for your contrapositive proof of n having to be a power of 2 for 2^(n) +1, I ... A: It is n that has to be a power of 2. If n has any odd factor e.g. n = s*t where s is odd then f(2^t) ... | |
| sums of 2 addends of same parity | 3/6/2008 |
| Q: please tell me if you are familiar with this, or have reason to believe it holds or is false, ... A: I elected to answer this question, even though I have never come across this before. If I wasn't ... | |
| possibilitys | 3/5/2008 |
| Q: what are all the possiblity of a 4 digit number using 0123456789 A: If repetition is allowed, each digit may be chosen in 10 ways, so there are 10^4 ways. If repetition ... | |
| inverting fractions | 3/4/2008 |
| Q: why fractions have to be inverted to perform dividion? just my cureosety. A: This about inverses. How do you do the opposite of dividing by 2. You multiply by 2. It brings ... | |
| Simple Solution | 3/1/2008 |
| Q: Here is myAn employee can retire from his place of employment if he meets the following ... A: Sorry for the delay. I didn't receive an email. My ISP is experimenting with a new method of spam ... | |
| A Maths Mindbender... | 2/7/2008 |
| Q: There's a bus with 7 girls. Each girl carries 7 bags. Each bag carries 7 big cats. Each big cat ... A: Sorry for the delay. I didn't get the email. We will assume that the girls each have 2 legs. Girls ... | |
| Pre Alg | 2/5/2008 |
| Q: Nth term My son was given the 2 problems to solve 1/7 2/9 3/11 4/13 came up with the expresion ... A: Sorrry for the delay. I didn't get the email. You have to notice what the pattern is. Each time ... | |
| day of the week | 2/3/2008 |
| Q: January 1, 2023 will fall on what day of the week? A: If you just want an answer, the simplest way is to type the date 1/1/2023 in an excel or open office ... | |
| Question on eye color gene | 2/2/2008 |
| Q: My mother has hazel eyes and my father has dark brown eyes. Out of 3 children they had 2 dark brown ... A: There is a problem about which genetic model of eye colour you are expected to use. The actual ... | |
| infinity | 1/29/2008 |
| Q: I had two problems and these are still remains from last 3 years. one is: sigma 1/n where n tends ... A: Let me explain sum to infinity. No one is suggesting we add an infinite number of terms. But the ... | |
| Number Theory | 1/25/2008 |
| Q: 1) Prove that if n>0 & (n^3)+1 is prime, then n=1 A: n^3 + 1 factorises as (n+1)(n^2 -n + 1) If it is prime, one of these factors must be 1. It is not ... | |
| number theory | 1/24/2008 |
| Q: please see the following questions and answer and help me. 1. Show that the square root of a prime ... A: 1. Suppose to the contrary Then root(p) = a/b with (a,b) = 1 p = a^2/b^2 a^2 = p*b^2. Since (a,b) = ... | |
| Set Theory Formulae | 1/22/2008 |
| Q: Could you please provide me with the formulas used in Set Theory..I'll be really grateful. Thanks ... A: I'm not going to reinvent the wheel. You should find everything you need to know at: ... | |
| number theory | 1/18/2008 |
| Q: please kindly help me. 1. Let a1,a2,…,an be positive integers, if a1,a2,…,an are pair wise ... A: I presume the notation [ ] means lowest common multiple. When we multiply the numbers together, the ... | |
| euclidean | 1/18/2008 |
| Q: Respected sir, I am navya. for ax = b (mod m)there is no solution if d does not divides b. where d = ... A: The equation can be written; ax = b + km a and m share the factor d =(a,m) so b must also have this ... | |
| Difference | 1/16/2008 |
| Q: I had the doubt on the following: What is the exact difference between Proposition, theorem and ... A: A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," ... | |
| Sequence | 1/4/2008 |
| Q: How to find the next term in a sequence? Is there a general rule? For example, the seqeunce ... A: The easy answer is that it could be any number you can think of. But usually we want the given ... | |
| Rates | 1/3/2008 |
| Q: Which or what answer is mathematical correct in the following regarding these rates? One worker can ... A: Now I come to read your query again, I realise that there wasn't an original question. If the ... | |
| fermat | 1/3/2008 |
| Q: I came to know that, the number of digits of a fermat number can be found by 1 + floor function of ... A: Here is a copy of a spreadsheet with F(n) worked out( only approximately for n>5), and the number of ... | |
| number theory | 12/31/2007 |
| Q: What do you mean by "Sloane's A000045)." Is it person name or any thing? please giveme reply. ... A: Sloanes is an encyclopaedia of integer sequences, each one numbered. A sequence with such a low ... | |
| gcd | 12/30/2007 |
| Q: I recently came to know for finding GCD of two numbers by the following formula. But I do not know ... A: This is just about impossible to explain without the ability to draw diagrams. The proof by Marcelo ... | |
| fibonacci | 12/30/2007 |
| Q: How to prove that ' The sum of alternative Fibonacci numbers ending with F_k is (F_k+1)-1. Please ... A: The point is that your alternate terms end with F(k). If k is even, we need to start with F(2). For ... | |
| fibonacci | 12/28/2007 |
| Q: I am mahima. 1,1,2,3,5,8,13,21,... is said to be fib series. here ratios are, 1/1 =1, 2/1 = 2, 3/2 = ... A: The golden ratio, phi, is the limit of the ratio of successive terms. It's value is (1+root5)/2 = ... | |
| fibonacci | 12/27/2007 |
| Q: I am mahima with fibonacci problem. please answer or give some solution to go ahed of tjhe problem. ... A: I have produced a spreadsheet to help with the investigation. If you give me your email address, I ... | |
| fibonacci | 12/27/2007 |
| Q: I am mahima with fibonacci problem. please answer or give some solution to go ahed of tjhe problem. ... A: I've already proved that the series is finite for base 2 and 3. I can't see any purely analytic ... | |
| fibonacci | 12/21/2007 |
| Q: please see the following and answer. how about converting the Fibonacci numbers to a base other than ... A: This sounds like a long term project rather than a question. However, I can start you off on it. In ... | |
| Convert from hexadecimal notation to binary notation | 12/14/2007 |
| Q: 1. 80E 2. 135AB 3. ABBA 4. DEFACED Please show work. Is this related to BASE calculations? If I can ... A: Each Hex digit is represented in binary by 4 binary digits. This is because 16 = 2^4. I am sure you ... | |
| Solve the congruence | 12/14/2007 |
| Q: Solve the congruence 4x=5(mod9) 2x=7(mod17) There isn't a key on the computer for the triple (=) ... A: I am sorry if I didn't do all the explanation you needed, but I assumed you knew about the group ... | |
| Interest | 12/14/2007 |
| Q: I have a question that I hope you can help solve. An investor wants to separate $30,000 into two ... A: I think I am getting quite good at no-algebra solutions. Suppose he invests all the cash at 2%. He ... | |
| numbers | 12/13/2007 |
| Q: Sir, see the following: For every positive integer n, there are n consecutive integers that are ... A: Your formula is not the only way to find prime deserts. Your example starting at 90 shows that. ... | |
| Solve the congruence | 12/12/2007 |
| Q: Solve the congruence 4x=5(mod9) 2x=7(mod17) There isn't a key on the computer for the triple (=) ... A: Have you met the Julia set in chaos theory? This can be solved by the Chinese remainder theorem, but ... | |
| divisibility | 12/11/2007 |
| Q: We know that 1331 is divisible by 11. for conformation, we can also use that divisibility test 11. ... A: For divisibility by d, you used base d-1, and the 11's rule. I suggested that instead, you could use ... | |
| divisibility | 12/10/2007 |
| Q: We know that 1331 is divisible by 11. for conformation, we can also use that divisibility test 11. ... A: You are using base d-1 to test for divisibility mod d. d-1 = -1 mod d (d-1)^2 = 1 mod d (d-1)^3 = -1 ... | |
| Number Theory | 12/5/2007 |
| Q: Prove that n^4+1 cannot be a prime number. A: I think you have mistyped this. 2^4 + 1 = 17 is prime. So is 6^4 + 1 = 1297. What I think the ... | |
| number theory | 12/3/2007 |
| Q: Sir, Please answer the below 2 questions. pl z. 1. Prove that there is no polynomial f(n)with ... A: 1. Suppose to the contrary. Then f(x) of degree n is prime for all integral x. Then f(0) = p where p ... | |
| Justify | 11/26/2007 |
| Q: Sir, How can we justify that: In every set of ten different 2-digit positive integers, a)There ... A: I can help with the first one. a) This is proved by the pigeonhole principle. The maximum possible ... | |
| Complex no. Problem | 11/25/2007 |
| Q: I came up with the following proof.Plz tell me whats wrong. Its here.(Consider i as iota) i^2 = -1 ... A: You have made a very common mistake, which many of my students do all the time. 'taking square root' ... | |
| real analysis | 11/25/2007 |
| Q: what is/are the proofs that rational numbers are a field? ANSWER: Hello Brendz First we have to ... A: To be an ordered field, the field has to include a set P of positive elements which is closed under ... | |
| N. Theory | 11/24/2007 |
| Q: Mr. Vijilant, I hope you are doing good and this is my last question for the year. If k = 2^50 ... A: This is not an easy question, and I don't believe it has an analytic answer since it deviates from ... | |
| Twin prime separation | 11/24/2007 |
| Q: I am mahima and I came with the following questions. Please give me a comprehensive solution for the ... A: I don't think I can help you on this one. You don't say what n1, n2 etc are. From your formula it ... | |
| High School Math | 11/23/2007 |
| Q: Sir, How are you doing? 1a) Our class of 16 people must elect a president, vice- president, ... A: This question is easy enough if you know the method. 1A We consider one possible combination of 24 ... | |
| Problem Solving | 11/23/2007 |
| Q: Mr. Vijilant, what is wrong with the following problem situation? A survey of 144 new teachers ... A: Using E for Europe, S for Asia and F for Africa, and applying the Venn diagram law. n(EUSUF) = n(E) ... | |
| High School Math | 11/23/2007 |
| Q: Sir, How are you doing? 1a) Our class of 16 people must elect a president, vice- president, ... A: I assume you are familiar with arrangements and selections. 1(a) The P can be elected in 14 ways. ... | |
| Number Theory | 11/17/2007 |
| Q: Could you help me with the following question please? 1) find the number of four- digit numbers ... A: That looks like two more questions. I've only time for one tonight. I'll try to get back to you ... | |
| Number Theory | 11/17/2007 |
| Q: Could you help me with the following question please? 1) find the number of four- digit numbers ... A: Sorry, I thought you would understand the notation. nPr denotes the number of permutations of n ... | |
| Number Theory | 11/14/2007 |
| Q: Could you help me with the following question please? 1) find the number of four- digit numbers ... A: Sorry abou the delay. I didn't receive an email. (a) 5^4 = 625 (b) 5P4 = 120 (c) 3*5^3 = 375 (d) ... | |
| induction question | 11/14/2007 |
| Q: having trouble with the proof. Prove that if n>=1 then, sqrt(1)+sqrt(2)+...+sqrt(n) > ... A: Sorry for the delay. I didn't get an email. I don't think this is one you can prove easily by ... | |
| triplet | 11/11/2007 |
| Q: Sir, Thank you very much for my previous question. Now, please answer the following. Prove that ... A: I presume you mean the product of the elements of the triple. We need consider only primitive ... | |
| real analysis | 11/11/2007 |
| Q: what is/are the proofs that rational numbers are a field? A: First we have to have an additive group. The rationals form an additive group because: 1. addition ... | |
| Triplet | 11/10/2007 |
| Q: Sir, I am Mahima and I have 2 questions in this time. Please answer . 1. Is there a formula to ... A: This is a standard question, and there is a proof in almost all number theory text books. There are ... | |
| Squarefree Number Theory | 11/9/2007 |
| Q: If b^2 is the largest square divisor of n, then a^2|n implies a|b A: Using the facts from you previous question, n = b^2*q where q is a prime or product of primes or ... | |
| Squarefree Number Theory | 11/9/2007 |
| Q: An integer is called squarefree if it is not divisible by the square of any prime. Prove that for ... A: Consider the unique prime factorisation of n. For each prime whose index is even, e.g. p^(2k), then ... | |
| Triplet | 11/9/2007 |
| Q: Sir, I am Mahima and I have 2 questions in this time. Please answer . 1. Is there a formula to ... A: 1. Yes there is a formula for all Pythagorean Triples. A primitive triple is one where there is no ... | |
| Disibility by 9 and 11 | 11/7/2007 |
| Q: First the question is working on mod 9 and mod 11. 2x99561=[3(523+x)]^2 On the left hand side I ... A: I'm not sure what you did on the right hand side. It is 3^2*(523+x)^2. The 3^2 = 0 mod 9, so we ... | |
| Cantor's diagonal method | 11/3/2007 |
| Q: can you please explain Cantor's diagonal method? thanks A: There are two different interpretaions of this. The countability of the rationals and the ... | |
| Simple Solution | 11/3/2007 |
| Q: I have a question that I believe you can answer. The answer should be determined without using any ... A: Yes, I think the following method could be done completely mentally. The LCM of 8,10 and 12 is 120. ... | |
| Properties of Congruence | 11/1/2007 |
| Q: For n>= 1(n is greater or equal to 1) use congruence theory to establish: 27|2^5n+1 + 5^5n+2. I ... A: I am afraid there is a misprint somewhere. it doesn't work when n=1. The expression evaluates to ... | |
| Halloween Question | 10/22/2007 |
| Q: 8 quarts of cider were left in the punch bowl after the Halloween party. If, in addition to the ... A: One way to do this would be the following: we start with 8,0,0 fill the 3q and empty into the 5q We ... | |
| statistics | 10/21/2007 |
| Q: A set of seven different positive integers has mean and median both equal to 20. What is the largest ... A: To make one of the values as large as possible, we make the 3 numbers smaller than 20 as small as ... | |
| Number Theory | 10/20/2007 |
| Q: I have some questions on number theory. Can you help? 1) For which positive integers,n , is the sum ... A: In fact, we only need to consider one of the primes, since in multiplications and divisions with ... | |
| Number Theory | 10/16/2007 |
| Q: I have some questions on number theory. Can you help? 1) For which positive integers,n , is the sum ... A: 1) The sum is n(n+1)/2 , and this is to be a factor of n! If n+1 is prime, this will not be a factor ... | |
| Divisibility | 10/16/2007 |
| Q: a) Do there exist natural numbers m,n such that 7/17 = 1/m + 1/n ? b) Let p be a prime number. For ... A: a) The answer here is no. Clearing the fractions 7mn = 17(m+n) So either or both of m,n is a ... | |
| Trig Identities | 10/14/2007 |
| Q: not sure if this question fits in the number theory category, but last year my maths teacher at ... A: It's not Number theory, but I promised to answer any Math question from a McAuley pupil. There's not ... | |
| DIVISIBILITY THEOREM | 10/11/2007 |
| Q: Respected Sir, I would like to know about the main theorem of divisibility by 3,, as in 3 is ... A: This is based on what is called modulo arithmetic. Here the modulus is 3. Two numbers are congruent ... | |
| Nth Term | 10/9/2007 |
| Q: theFind the rule for the n-th figure. Then find the number of tiles in the 200th figure. the 1st ... A: Did you notice that each diagram has 4 more tiles than the previous one. A sequence that you know ... | |
| number theory | 10/9/2007 |
| Q: please see the following. 1. If p is an odd prime, let q = (p-1)/2 prove that (q!)^2 + (-1)^q is ... A: Now you are testing me. You didn't even tell me what the expression was congruent to. But I know ... | |
| diophantine eqts. | 10/8/2007 |
| Q: Has anything been done on the nth degree pellian eqt. : X^n - AY^n = 1 where A>1, X,Y,n,A are in N ... A: I'm not sure that much has. It took long enough to sort n=2 completely satisfactorily. I did find a ... | |
| congurance | 10/8/2007 |
| Q: please see the problems on congurences. 1) Let f be an integer-valued arithmetical function such ... A: 1) You haven't asked a question here. 2) The number n! is divisible by 2, but not by any other ... | |
| Decimals & Fractions | 10/1/2007 |
| Q: Can you explain why or how the fraction 1/3 in 0.25 1/3 occupies the 1/100 place along with the 5 ... A: I am a number theory expert, not a business maths expert. Business people have their own funny ... | |
| Decimals & Fractions | 10/1/2007 |
| Q: Can you explain why or how the fraction 1/3 in 0.25 1/3 occupies the 1/100 place along with the 5 ... A: I think the confusion arises because the notation you have used is not an accepted one. All the ... | |
| Decimals & Fractions | 10/1/2007 |
| Q: Can you explain why or how the fraction 1/3 in 0.25 1/3 occupies the 1/100 place along with the 5 ... A: I'm not sure I understand the question. Do you want to add 0.25 + 1/3. If so, you need to convert ... | |
| square | 9/29/2007 |
| Q: Q: If n is a natural number less than 100 and k is whole number ,for how many values of n, n^2=24k+1 ... A: I am always pleased when someone comes back with a follow-up. It means they are really thinking ... | |
| square | 9/28/2007 |
| Q: Q: If n is a natural number less than 100 and k is whole number ,for how many values of n, n^2=24k+1 ... A: You certainly have a good starting point. As long as n is odd, the square is of the form 8m+1, so ... | |
| number theory | 9/27/2007 |
| Q: Sir, Please see the following. Now I am asking not more than 3. pleaseeeeeeeeeee answer sir. 1. ... A: You do right to ask for clarification. WOLOG is a quick way of saying 'Without loss of generality'. ... | |
| Fibonacci sequence | 9/27/2007 |
| Q: For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the ... A: If the 6th and 7th are a and b, then b^2-a^2 = 517= 11*47 = 1*517 Using the factors (b-a)(b+a) one ... | |
| number theory | 9/27/2007 |
| Q: Sir, Please see the following. Now I am asking not more than 3. pleaseeeeeeeeeee answer sir. 1. ... A: 1) This is much more difficult to show than to prove there are an infinite number of primes of the ... | |
| number theory | 9/26/2007 |
| Q: I am mahima asking again with following problems. please solve and show me. (1) Show that there are ... A: You are getting on to quite difficult work. 1) n!-1 is odd, so is divisible by at least one odd ... | |
| congureance | 9/26/2007 |
| Q: Again I had the following please do it. 1)Show that if f(x)is a polynomial with integral ... A: That's a lot of questions! 1) Each term in the first polynomial b*a^n is congruent to the ... | |
| congurence | 9/26/2007 |
| Q: prameela here. please see the following and give answer <1> Let a,b,m,n belongs to Z with m>0 and ... A: 1) Write m=nk a=b mod m implies a-b = tm =(tk)n implying a-b mod n. 2) a-b = tm, a-b = sn. ... | |
| Number theory | 9/25/2007 |
| Q: What is the sequence of these numbers? 7,17,34,55 A: With so few terms, many sequences could start like this. One that does work (and the simplest ... | |
| congurence | 9/23/2007 |
| Q: If (a, m) = 1 then there is an x such that ax is congruent to 1 (mod m). Any two such x are ... A: Helo mahima Elements 1,a,a^2,... form a group under multiplication mod m. Let a^r be the smallest ... | |
| Number Theory | 9/23/2007 |
| Q: I'm having trouble getting started on a few problems prove/disprove a^2|b^3, then a|b. a^2|b^2, ... A: All of these are proved by considering the unique prime factorisation of a and b. Let p be any prime ... | |
| primes... | 9/20/2007 |
| Q: I am pavani. see the following! 1. Prove that 2 + square root of (-6) and 2 - square root of (-6) ... A: You are certainly making progress! These are complex numbers, and an important property of a complex ... | |
| numbers and theory | 9/20/2007 |
| Q: Navya here. Please see the following question and solve it. (1) What is the largest number of ... A: 1) Every 4th integer is a multiple of 4, so you can't have more than 3 consecutive square free ... | |
| Functions | 9/20/2007 |
| Q: Two functions are defined as follows: F(x) = x2+8x-18 and G(x) = 3x-6-x2. IF H(x) = ... A: You need to find where the functions have equal values. That is at x=-4 F(x) = G(x) = -34 and ... | |
| merrsenne | 9/20/2007 |
| Q: I had the following doubt. In my tet book the following theorem given but proof not given in the ... A: I realise that I didn't read the question carefully enough. I proved that Mp was of the form 2kp+1. ... | |
| need help with homework | 9/20/2007 |
| Q: Do you know anything about In-Out table. I'm a 9th grader in Highschool. Have you ever hard of ... A: I'd never heard of this before, but searching the web suggests to me that it is just a table of ... | |
| fibnoci and lucas | 9/19/2007 |
| Q: Sir, In the Binet’s used in his Formula, phi^2 + phi =1. But Phi = 1.6180339887499… When we put ... A: You don't have the correct formula. It is phi^2 - phi =1. 1) This can be proved by induction. It ... | |
| Fibbonacci Numbers | 9/18/2007 |
| Q: Please explain the following. n Find a formula for sigma Fi. ... A: To do this one you need to know the formula for F(n). It is (phi^n - (1-phi)^n)/5^(1/2) where phi = ... | |
| divisions | 9/17/2007 |
| Q: I am prameela. I am doing number theory by your motivation and help in this subject. I cannot forget ... A: You are making me work very hard asking multiple questions. Please don't ask more than two ... | |
| number theory | 9/17/2007 |
| Q: I came with new/diffrent problems. Please go throgh this and solve for me... 1) Prove that there are ... A: I hope you have been having a go at doing these for yourself. 1)Recall that a|b implies a|a+b and ... | |
| plez | 9/17/2007 |
| Q: you never given help in my studies. I am so sad in this part. As an expert why you are not showing ... A: Let a and b be two distinct elements in S. Then a|b and b|a. This means a=b, a contradiction. So ... | |
| n-theory | 9/17/2007 |
| Q: Sir, I am navya, I had the following 2 problems, which are eating my brain. please help me. 1. Let ... A: There is something strange about 1. What do the commas mean? Should there be P(n+1)? 2. Write ... | |
| number theory | 9/17/2007 |
| Q: I came again with 3 problems. (1) Prove that every positive integer n, there are n consecutive ... A: 1) The n integers (n+1)!+r as r goes from 2 to n+1 all have the factor r. e.g. n=4. 5!=120. The ... | |
| numbers | 9/14/2007 |
| Q: What is the sum of all 7 digit numbers using four 1's and 3 zeroes Its getting lenthier .... A: The number of arrangements of n things when p are alike of one kind and q alike of another kind is ... | |
| number theory problems | 9/12/2007 |
| Q: Can you help me with these problems please. Find the value of: Show that every positive integer can ... A: This was quite a difficult problem. We choose the largest prime p that is less than or equal to n. ... | |
| Decimal Fractional Numbers | 9/12/2007 |
| Q: Why do mathematicians dislike decimal fractional numbers? Here is an example: 0.66666..... is ... A: If a mathematician (especially an applied mathematician) is only interested in a final numerical ... | |
| number theory problems | 9/12/2007 |
| Q: Can you help me with these problems please. Find the value of: Show that every positive integer can ... A: This is simply writing the number in base 2. We can just write down the highest power of 2 less ... | |
| series | 9/11/2007 |
| Q: How R U? Sir,please tell me your date of birth... See the my new doubts and solve for me. A) The ... A: I can only make a conjecture at present. I suspect that if a is odd the gcd is 2, and if a is even ... | |
| Number theory | 9/10/2007 |
| Q: I am navya from india. I am studying number theory with your inspiration. while studying this I got ... A: I help people to understand Mathematics for free for a number of reasons. Firstly I am a committed ... | |
| series | 9/10/2007 |
| Q: How R U? Sir,please tell me your date of birth... See the my new doubts and solve for me. A) The ... A: There is still a lack of brackets here. a^2^m can mean (a^2)^m or a^(2^m). These are not the same. ... | |
| series | 9/10/2007 |
| Q: How R U? Sir,please tell me your date of birth... See the my new doubts and solve for me. A) The ... A: A) This simply depends on the fact that (a+b,a)=(a,b) and (A1,A2)=1. You could set out a formal ... | |
| Number theory | 9/10/2007 |
| Q: I am navya from india. I am studying number theory with your inspiration. while studying this I got ... A: 1) If n is even then it is the sum of 4 and n-4, both even and therefore composite. If n is odd, it ... | |
| divisions | 9/10/2007 |
| Q: Sir, I am Mahima. Please see the following. 1) For each of the following give a proof with counter ... A: (a) Write (a,b)=h and a=sh,b=th then (s,t)=1 b^n/a^n=t^nh^n/(s^nh^n)=t^n/s^n is an integer. ... | |
| nth terms in sequences | 9/9/2007 |
| Q: it says generate the first 10 terms of these 1)n squared + 5 2)2n squared + 5 3)n squared + 10 4)4n ... A: It is just a matter of plugging in the numbers 1 to 10 for n. I will work out the first three of ... | |
| Sexagesimal | 9/9/2007 |
| Q: How would I use the Sexagesimal system? Unlike the decimal system where each step up is a multiple ... A: Sexagesimal is base 60, but we don't use 60 different symbols for the digits. Instead base 10 is ... | |
| number theory | 9/8/2007 |
| Q: please see the following and give me a solution 1) For integers a,b with b < 0, show that b < a mod ... A: I asked you to try an example of these. This is the only way you are going to make progress. Take ... | |
| doubts | 9/7/2007 |
| Q: Sir, What do you mean by conjecture? Is it theorem or ... Also, I have very big doubt in my mind. ... A: A conjecture is simply a guess. In other words a theorem that seems to be correct but for which ... | |
| solution of problem with venn diagram | 9/6/2007 |
| Q: Out of 200 students, 50 of them takes discreate mathematics, 140 of them takes economics and rest ... A: Your question is still not making sense. If 30 take both DM and P, how can only 10 take P? In your ... | |
| sum of squsres | 9/6/2007 |
| Q: In how many ways a number can be written as the sum of two sauares? for example: 5 = 1^2 + 2^2; ... A: There is a simple formula for the number of ways. First factorise the number into the form ... | |
| solution of problem with venn diagram | 9/5/2007 |
| Q: Out of 200 students, 50 of them takes discreate mathematics, 140 of them takes economics and rest ... A: The question is not clear. It mentions both courses, but there seem to be 3 different courses. ... | |
| numbers | 9/3/2007 |
| Q: Imagine that the digit 7 has been banned from use for superstitious reasons. So what would call "the ... A: Since one digit is missed out, this notation must be very similar to base 9. Checking easily shows ... | |
| problem about counting | 9/3/2007 |
| Q: How many terms are contained in (a+b+c)^20? A: I have to assume you mean different terms. If the index of a = ind(a) is 0, then ind(b) has 21 ... | |
| number theory | 9/2/2007 |
| Q: good evening. Thank you for answering the previous questions. Please answer the following problems. ... A: All of these are self-evident and do not need proof. Z is the set of integers, so that a is an ... | |
| induction | 9/2/2007 |
| Q: I am pavani. I had the doubt(s) in induction. please clarify with examples. 1. What do you mean by ... A: 1. The weak version is: Given a theorem T(n), T(1) true and T(k) true implies T(k+1) true, then ... | |
| numbers | 8/31/2007 |
| Q: How many integers between 1 and 1000000 have the sum of digits equal to 18? What is the generalzed ... A: I've just found this in the question pool. The integers all must be multiples of 9, but that doesn't ... | |
| theory of numbers | 8/30/2007 |
| Q: sir, I came again to know the folowing problems. ax^2 + 2bxy + cy^2 is a polynomial. when a, 2b, c ... A: Consider any one prime p which is a factor of both a and b. a = ...p^x.... and b = ....p^y... in ... | |
| Proofs | 8/29/2007 |
| Q: Can you please help me withe following: Is it True or False and prove it: 1)A+BC=(A+B)(A+C) i ... A: This isn't number theory, it is Boolean Algebra, the algebra of logic. The symbols represent the ... | |
| 6 digit combo | 8/29/2007 |
| Q: What is the total number of combinations on a lock?? (digits 0-9) A: Note that although the usual phrase is 'combination lock', it is actually a permutation lock since ... | |
| divisions. | 8/28/2007 |
| Q: I did not undrestand these questions. please help me. 1. if (a,b) =1 then (a^n,b^k) =1 for all n>=1, ... A: 1. The only factors of a^n are a,a^2,a^3...a^n The only factors of b^k are b,b^2,b^3...b^k. These ... | |
| theory of numbers | 8/28/2007 |
| Q: sir, I came again to know the folowing problems. ax^2 + 2bxy + cy^2 is a polynomial. when a, 2b, c ... A: 1. It is not possible to find a polynomial that gives only prime values. 2. This is obvious if ... | |
| number theory area | 8/27/2007 |
| Q: I am Mahima came again with 3 questions. please solve and encorage me in my studies. 1. how to prove ... A: These questions are basic book knowledge which can be found in any number theory book or a tutorial ... | |
| do it | 8/27/2007 |
| Q: i am navya.Does there always exist atleast one prime between n^2 and n^2 + n for every integer n>1? ... A: This is an unsolved problem of number theory. In fact, also unsolved is the weaker bound. There ... | |
| number theory | 8/26/2007 |
| Q: what is the algebraic solution for x, y, z to the following eqn : x^3 + y^3 = z^3 + 1 A: I don't know one, and I haven't been able to find one. However, if you go to ... | |
| Ages | 8/24/2007 |
| Q: Hey Raja, this is more of a riddle than a math question however I think you will be smart enough to ... A: I have had another look at the problem, and as long as you have typed the riddle exactly as in the ... | |
| Probability | 8/24/2007 |
| Q: I'm very grateful for the solutions to my previous questions.Your approach to the problems have been ... A: DPAB is a re-entrant quadrilateral like an arrow head, so the probability is zero. If this was a ... | |
| Base | 8/23/2007 |
| Q: Find, as a proper base ten fraction, the sum of the following infinite series of repeating decimals, ... A: Perhaps it is easier to consider 0.999999999.... You would have to agree that this is the same as ... | |
| Remainder | 8/23/2007 |
| Q: Find the last 3 digits of 7^347 I know we can get ans by dividing the no by 1000,but no theory is ... A: 7^4 = 1 mod 5 by Fermat's theorem. In fact 7^4 = 2401 =1 mod 100. We need to find the smallest ... | |
| Base | 8/23/2007 |
| Q: Find, as a proper base ten fraction, the sum of the following infinite series of repeating decimals, ... A: This is a lot easier than you imagined. Consider the number .0999... in base 10. It is just another ... | |
| Rates | 8/21/2007 |
| Q: If ten workers perform one job in 5 days, one person performs one job in how many days? Here is ... A: You seem to be multiplying workers X jobs X days. This not the method. We multiply workers by days ... | |
| numbers | 8/20/2007 |
| Q: please solve the folowing ones., 1) For integers a, b with b <0, show that b<a mod b < or = 0. 2) If ... A: 1. I have never seen a mod b with b<0. However, a mod b is just the same as a mod -b. The problem ... | |
| general | 8/20/2007 |
| Q: sir, I am MAHIMA from india. I had the following questions. please answer thease as early as ... A: 1. If n is a square, its square root is the number required. If not it factorises into two factors ... | |
| number theory | 8/15/2007 |
| Q: I cam back. How are you? I am fine. I hope you are also fine. I had the following quarries. please ... A: I will try to explain the meaning of each of these terms by means of an example. A theorem is a ... | |
| Probability | 8/15/2007 |
| Q: A circle contains 2006 points chosen so that the arcs between any two adjacent points are equal. ... A: The total number of triangles is 2006C3. For a right angled triangle, the hypotenuse is a diameter. ... | |
| raising 2005 to the power 2005 | 8/13/2007 |
| Q: When written as a decimal number, 2005^2005 has D digits and leading digit L. Find D + L. A: We start by taking the log to base 10 of the number and using the laws of logs. This gives ... | |
| how to solve these type of problems | 8/7/2007 |
| Q: good evening sir, I am one of the very intrested one who want to learn number theory properly. I had ... A: Every child in junior school knows the division algorithm but almost certainly doesn't call it that. ... | |
| proove it | 8/7/2007 |
| Q: Reapected sir, I came again to get help from you. How r U sir? why u r not available from last 1 ... A: I was on holiday last week with no internet access. 1. You have probably used (a,b) = (a,b-a). This ... | |
| Numbers | 8/6/2007 |
| Q: How many integer solution exists for |x|+|y|+|z| = 15 Pls help on this..how do i proceed..taking 1 ... A: I have just found this in the question pool. The best way is to think geometrically. The points are ... | |
| Ages | 8/6/2007 |
| Q: Hey Raja, this is more of a riddle than a math question however I think you will be smart enough to ... A: Your answer is not correct because Jim is 36 and that is 3 times as old as your value for Sid's age ... | |
| Numbers | 7/27/2007 |
| Q: How many natural numbers having at most six digits have the sum of their digits as at most six? A: We first choose a selection of 6 digits e.g. 122000 and then arrange them. A selection of n objects ... | |
| twins and sophie germain primes | 7/24/2007 |
| Q: sir, so far do we know of any relation between twin primes and sophie germain primes? given the ... A: It has not been proved that there are an infinite number of either of these. Attempts have been made ... | |
| primes in algebraic series | 7/22/2007 |
| Q: sir, just like we have twin primes (p, p+2) cousin primes (p, p+4) sexy primes (p,p+6) sophie ... A: I am sorry to say, very little. I am not aware of any work done on this subject. It has not even ... | |
| integer sequences | 7/17/2007 |
| Q: My question concerns the numbers produced by two different sequences. I am wondering if it is ... A: This is a fascinating problem. I assumed from the example that a and b had to be positive integers. ... | |
| integer sequences | 7/16/2007 |
| Q: My question concerns the numbers produced by two different sequences. I am wondering if it is ... A: No-one has asked me one like this before. Such an equation is called a Diophantine equation after ... | |
| maths subject | 7/16/2007 |
| Q: I am trying to find out the name of a particular mathematics subject. But I do not know what it is ... A: I don't think there is a name for the topic, but it comes up in most algebra courses. You may find ... | |
| Unique numbers | 7/15/2007 |
| Q: I have a list A of unique numbers of 9 digit each. I generate another list B by interchanging right ... A: First, about the 1:1 transformation. Of course, squaring is not 1:1 if the domain is the set of ... | |
| Rates | 7/14/2007 |
| Q: Here is myIf 15 workers can perform a piece of work in 7 days, each worker performs what fractional ... A: We have to assume here that each worker does the same amount of work, and that each does the same ... | |
| Unique numbers | 7/14/2007 |
| Q: I have a list A of unique numbers of 9 digit each. I generate another list B by interchanging right ... A: We must assume that the interchange retains the order of the two blocks of digits. If the left 4 ... | |
| Application of number theory | 7/9/2007 |
| Q: Do you know what are applications of number theory other than cryptography? Thank you, Frans ... A: This must be a very common problem. If you can apply theorems when you have worked examples at hand ... | |
| Application of number theory | 7/8/2007 |
| Q: Do you know what are applications of number theory other than cryptography? Thank you, Frans A: I don't know of many, but I have chosen the Chinese Remainder theorem as an example. It was ... | |
| number theory pattern question | 6/8/2007 |
| Q: whatsw the next three terms of the pattern: 4,6,9,10,14,15,21,22,25,26,33,34,35,38 i am thinking the ... A: Well done! These numbers are called semiprimes. Of course, since there is no formula for the nth ... | |
| number theory | 6/4/2007 |
| Q: how r u? I hope you are fine. according to your valuble suggextions, I am studying number theory ... A: A Mersenne prime is a prime of the form 2^n - 1. If n=3, we have the mersenne prime 7. To each ... | |
| Box Principle | 5/23/2007 |
| Q: Good Evening! I'm having a problem with these two numbers, basically I have an idea but I don't ... A: I can now help you with your third question The subset must contain one at least of the pairs 1,2 ... | |
| math problem | 5/15/2007 |
| Q: the diagram is one of a graph of the function f(x)=(x^2)+1,-1<=x<=1 and p,q E(element) R.(i)find ... A: This problem was structured to get you to understand when a function had an inverse. Unfortunately, ... | |
| Interest Rates | 5/14/2007 |
| Q: The amount of $1.00 compounded annually at 4% for 5 years (5 periods) is $1.216653. For a principal ... A: Tables do not normally have units in them because it is wasteful of space to put the same unit in ... | |
| n-theory | 5/8/2007 |
| Q: sir, I would like to learn numbertheory from elementary to advanced level. please tell me the book ... A: I think you can use google or another search engine to find other sites yourself. If you have worked ... | |
| Number combinations | 5/7/2007 |
| Q: How many different combinations of 13579 can be generated and then rank them from lowest to highest. ... A: I think there is a problem with the language used here. The word combination refers to a selection, ... | |
| n-theory | 5/6/2007 |
| Q: sir, I would like to learn numbertheory from elementary to advanced level. please tell me the book ... A: I have just seen an inexpensive book Elementary Theory of Numbers (Dover Books on Advanced ... | |
| Fermat Difference of Squares | 4/27/2007 |
| Q: I have noticed that everyone solves Fermat's Difference of Squares by taking the square root of the ... A: Excellent. I have just done the analysis myself. (2m-1)^2 - (2m)^2 gives a number of the form 4k+1, ... | |
| Fermat Difference of Squares | 4/27/2007 |
| Q: I have noticed that everyone solves Fermat's Difference of Squares by taking the square root of the ... A: I am afraid that there is no way to know whether the number to be tested for primality can be ... | |
| need help | 4/25/2007 |
| Q: The Egyptians used the square of 8/9 of the diameter (=(8d/9)2) for the area of a circle. In ... A: Substituting for d =2r and squaring gives k = 256/81 This is approx 3.160493827 compared with PI ... | |
| math | 4/24/2007 |
| Q: Vijilant, Please help. I do not know how to solve 2 = 14x + 60y using Euclidean's algorithm. Wendy A: The Euclidean algorithm, or Euclid's algorithm is the method for finding the gcd of two or more ... | |
| powers and common multiples and or divisibility | 4/11/2007 |
| Q: my horrendously vague stab in the dark at a title in the subject line should take care of clarifying ... A: 1. No, this isn't true. Just consider 10 and 8. 10 = 2*5 and 8 = 2^3. 10 contains the factor 5, ... | |
| powers and common multiples and or divisibility | 4/10/2007 |
| Q: my horrendously vague stab in the dark at a title in the subject line should take care of clarifying ... A: This is an easy one to explain. There are no powers of two that are multiples of 10. This is ... | |
| probability of a specific digit sequence within irrational numbers | 4/7/2007 |
| Q: the probability that a finite sequence of digit like 1618033988749 is contained within a specific ... A: I am pretty sure that this has never been proved. There are quite a few web-sites with interesting ... | |
| prime pattern | 4/4/2007 |
| Q: vijilan. the question is: The smallest positive integer n for which the numbers n^2+1, n^2+3, n^2+7, ... A: I see what you mean by brute force. I can certainly improve the time very quickly by a factor of ... | |
| prime pattern | 4/3/2007 |
| Q: vijilan. the question is: The smallest positive integer n for which the numbers n^2+1, n^2+3, n^2+7, ... A: I have thought about this again and have come to the conclusion that quadratic reciprocity may not ... | |
| prime pattern | 3/30/2007 |
| Q: vijilan. the question is: The smallest positive integer n for which the numbers n^2+1, n^2+3, n^2+7, ... A: This is most definitely a research question and one which I can't answer right away. You haven't ... | |
| number theory | 3/28/2007 |
| Q: Generate a random 200-digit number, what is the chance of getting a prime number? A: I am afraid I do not have the computing power to calculate this exactly, but I can estimate it using ... | |
| curious relationship | 3/19/2007 |
| Q: playing with some numbers I noticed a pattern and I was wondering what this was called and where I ... A: The process of summing the digits of a number repetitively until a single digit remains is called ... | |
| puzzle | 3/13/2007 |
| Q: you did not answer. The word is yo yo and each direction counts. What is the formula?i have a word ... A: I will have to assume that the arrangement is: YOYOY OYOYO YOYOY OYOYO YOYOY There is one YOYO in ... | |
| number theory | 3/5/2007 |
| Q: 1. Find all positive numbers x and y which solve the equation 41x 16y = 2000. 2. Find the ... A: The first one has a sign missing. I shall assume it is + Since 16 is a factor of 2000, write x=16X ... | |
| math | 3/4/2007 |
| Q: that's what i want the program for is to check the primes and if its programmable to save a file of ... A: I have found a book which contains and explains algorithms for testing and finding prime numbers. ... | |
| quadractic equations | 2/28/2007 |
| Q: Please help me solve these..if you can. choose a value for k so that the equation 5x^2-10x+7=k ... A: This is an exercise in completing the square. You should be able to complete the square on the LHS ... | |
| math | 2/26/2007 |
| Q: wrong e mail address I am looking for a program that can do math in large numbers over 10 million ... A: Sorry for the delay. I forgot to log my holiday. Mathematica can certainly deal with numbers with ... | |
| Fibonacci series | 2/1/2007 |
| Q: I have a conjecture if f(n) is the nth term of the fibonacci series, f(n-1) + f(n+1) -1 = 0 mod n ... A: I am delighted to tell you that I have now constructed a proof of your conjecture. L(n) = ... | |
| combinitorics question | 1/25/2007 |
| Q: a class of 10 boys and 15 girls are divided into five groups. how many different ways can the ... A: I don't claim that I am an expert on this topic but I can help you with your question. I assume from ... | |
| expectation | 1/19/2007 |
| Q: If you want to find the variance of X: let S denote each traingle in X, then you observe that Var(S) ... A: Apart from the mistype of = instead of -, I agree with your calculation of the variance of x in the ... | |
| expectation | 1/18/2007 |
| Q: One of my friends told me about your problem-solving skills. I am trying to solve this problem, ... A: I see no reason to doubt your first analysis. My first thought always in a tricky situation is to ... | |
| combinations from limited duplicative sets | 1/10/2007 |
| Q: I'm embarrassed to discover that I sent you a typographical error in the problem that I posed. The ... A: Yes, I thought it may have been a mistype. Now, (p+1)^2 has 21 factors, so must be of the form ... | |
| combinations from limited duplicative sets | 1/9/2007 |
| Q: Vijilant, I don't have a folow up question, but I just wanted to thank you for your answer to my ... A: The number of factors of a number is an example of what is called in number theory, a multiplicative ... | |
| combinations from limited duplicative sets | 1/8/2007 |
| Q: Suppose you have n objects, but only m are distinct. That is, there are n1 objects of the 1st kind, ... A: This is a combinatorics question which is not my field of expertise. I don't know a formula for ... | |
| 0.9r | 12/30/2006 |
| Q: ah thanks that clears up my last query, so if the limit of a recurring number is the number which ... A: This will have to be the last post on this topic. The limit of the series 0.9 + 0.09 + 0.009 +.... ... | |
| 0.9r | 12/29/2006 |
| Q: so are you saying that some mathematicians accept and use limits and others dont, or have I ... A: Mathematicians everywhere accept and use limits. What some disagree about is whether it is possible ... | |
| 0.9r | 12/29/2006 |
| Q: is the limit of a number just an idea that someone made up or is it actually something, lets say ... A: You are talking like a real mathematician:- being sceptical and not accepting anything without ... | |
| Cooking Measurements | 12/25/2006 |
| Q: Can you please tell me what 2 ounces are equaled to? A: If you are talking about weight, 1 ounce = 28.3495 gm. Since this is not a nice round number, if you ... | |
| primes | 12/22/2006 |
| Q: sir, What is the diffrence between reletive prime, twinprime and co prime. thanks. A: Two numbers which are relatively prime are numbers whose gcd is 1. For example 6 and 25. Neither ... | |
| number theory | 12/17/2006 |
| Q: need to know if i am going right.Prove by mathematical induction, that if a,b elements N then ... A: I've never used induction to prove this because (a^n+b^n)/(a+b) is the sum of a GP when n is odd. ... | |
| congruency | 12/16/2006 |
| Q: prove that 111*333+333*111 is divisible by 7. A: I am sorry to disappoint you. Perhaps you have mistyped the expression. 111 = -1 mod 7, so 333 = -3 ... | |
| numbers/euclid | 12/12/2006 |
| Q: Sir, I am Pavani. I don't know how to solve the following problems, please answer for me. 1. How to ... A: The Euclidean algorithm finds the gcd of two numbers by repeatedly replacing the larger with the ... | |
| Numbers with exactly 7 prime factors | 12/11/2006 |
| Q: Another similar question is : What is the smallest set of consecutive 3 numbers with 6,7 & 8 prime ... A: Once again, this does not seem to be a problem that number theory can shed much light on, except to ... | |
| primes | 12/8/2006 |
| Q: I am your student pavani. how are you? I got doubt in the folloing poblem. If the number is small, ... A: I am afraid there is no easy method to factor a product of large primes. Fermat used a trial method ... | |
| Average Number of Prime Factors | 12/6/2006 |
| Q: It seems to me that as an integer n increases, the chances increase that it will have many prime ... A: You are quite right in your conjecture that the chances increase as n increases. A few formulae are ... | |
| Numbers with exactly 7 prime factors | 12/5/2006 |
| Q: Is there a rule to determine all numbers that have exactly 7 prime factors ( say less than 1 ... A: When a number is written in Euclidean prime factor form as in your examples it is simple to add the ... | |
| theory of congruences | 12/3/2006 |
| Q: how can we verify that 0,1,2,2^2,2^3,.......,2^9 form a complete set of residues modulo 11.but that ... A: I don't know if you have any experience of elementary group theory, but if you do this is the ... | |
| theory of congruences | 12/2/2006 |
| Q: what is remainder when 41^65 is divided by 7 A: I can't type the congruence symbol, so will type = instead. 41 = -1 mod 7 41^2 =(-1)^2 = 1 mod 7 ... | |
| combinations | 12/1/2006 |
| Q: How many possible 6-digit number combinations can you make using the digits one through NINE? A: Assuming you are not allowed to repeat any digit and you are not interested in the order of the ... | |
| theory of congruences | 11/30/2006 |
| Q: prove that the integer 53 raised to 103 +103 raised to 53 is divisible by 39 A: The method is to prove it is congruent to zero mod 3 and also mod 13. 53 = 2 mod 3 53^2 = 4 = 1 mod ... | |
| reply2 : Circles | 11/24/2006 |
| Q: I downloaded the trial version of mathematica. It had the minimize function. I don't think i'm ... A: Perhaps your syntax wasn't quite right. I typed ... | |
| reply : Circles | 11/23/2006 |
| Q: Yay, your the only expert that actually thought about my question :) I understand the bit about the ... A: I loved that graphic. It's similar to the one I tried with winplot but better. I had a look in ... | |
| Circles | 11/23/2006 |
| Q: i couldn't find anyone else that could answer this: "this question has been denied by other ... A: This is certainly not a problem suitable for calculus because of the abs and sqr functions. Note ... | |
| Basic functions | 11/23/2006 |
| Q: I don't know exactly what number theory is exactly, but I figured you might best be able to answer ... A: I gave you the example of the Euler function which is relatively simple to explain; there are also ... | |
| Basic functions | 11/21/2006 |
| Q: I don't know exactly what number theory is exactly, but I figured you might best be able to answer ... A: Sorry for the delay in answering your question. I have been very busy marking exams. There are many ... | |
| Quadratic Residues | 11/9/2006 |
| Q: It makes perfect sense. Your argument can also be used to show that 3.2^(n-1))^3 is always a ... A: This is a bit easier than I thought it was going to be. The group is of order 12nk+6 =3(4nk+2) So ... | |
| Combinations of 3 | 11/8/2006 |
| Q: If I have 12 different items. How many different combinations of 3 items can I have? i.e. 12 ... A: The mathematical notation for this is 12C3. That is 12 choose 3. It is calculated as ... | |
| Quadratic Residues | 11/3/2006 |
| Q: I have strong evidence that (3.2^(n-1))^3 is always a quadratic residue of primes of the form ... A: I assume you are familiar with the quadratic reciprocity law, the legendre symbol, which I shall ... | |
| maths | 10/30/2006 |
| Q: what is the nth term of this number pattern 0 7 16 27 40 A: There are a number of different ways to look at the problem. The obvious approach is to look at the ... | |
| number puzzle | 10/18/2006 |
| Q: add numbers wheels on eight taxis even numbers up to ten numbers on one dice A: This is a question which is capable of several different interpretations, for instance does it mean ... | |
| Big O Notation | 10/17/2006 |
| Q: Can you help understanding the Big O notation. I have difficulties in determining the O notation of ... A: This is not really my expertise. The only time I remember using the notation in number theory was ... | |
| Divisibility Proof | 10/14/2006 |
| Q: I cannot seem to figure out the proof by contraposition for the following: For all integers a,b,and ... A: This is an interesting question, because it seeks to see if you understand the different types of ... | |
| base 10 | 10/13/2006 |
| Q: Why do we count on base 10? What are the advantages (other than having 10 fingers - I've never seen ... A: Historically, Im pretty sure you are right in thinking that it was a good system because for example ... | |
| Whole Numbers | 10/9/2006 |
| Q: What is the least number that leaves a remainder of 3 when divided by 5, a remainder of 2 when ... A: You didn't tell me what your mathematical background was, so I assumed you had met the modulus ... | |
| Proof | 9/27/2006 |
| Q: prove that for any m,n 'E'(element) N(nat.nos.) m not= n --> m^2+n^2>n^2 i tried this...(since m ... A: I think you may have mistyped the question. Since m^2>0 for n a natural number, m^2+n^2>n^2, so it ... | |
| Discrete Math | 9/21/2006 |
| Q: Your guidance was pivotal in getting a B on my last test and now I have another study guide I am ... A: Congrats on your B. I can't see how the hint helps. I looked at the ratio n!/40^n and what happens ... | |
| MAth | 9/17/2006 |
| Q: which number completes the sequence 2, 9, 5, 13, 10, 19, 17 Answer a. 22 b. 24 c. 25 d. 27 e. ... A: If we look at the pattern of differences; that is the difference, term - previous term we have: ... | |
| Math | 9/17/2006 |
| Q: someone asks you for a sum of money between 1 dollar and 5 dollars. I'm going to give you five ... A: Instead of using base 1 we use base 2. In the envelopes we put 1,2,4,8,16,32,64,128,256 and 512 ... | |
| number theory | 9/12/2006 |
| Q: two questions: 1. what is a sucessive product of a number called? 2. what is a name for a product ... A: There could be a number of different interpretations of both your questions. I am assuming that ... | |
| Number theory | 9/11/2006 |
| Q: Find the gcd (243,1025)unsing the euclidean algorithm, and express the gcd in terms of the original ... A: The Euclidan algorithm proceeds by successively dividing the most recent divisor by the most recent ... | |
| Days of the Week - Congruence | 9/10/2006 |
| Q: I was so happy and suprised to get such a quick response. When I worked on the problem, I also ... A: I covered the point about differences in my reply. The point is that there are 4 years in every 28 ... | |
| set theory | 9/9/2006 |
| Q: there are 50 people ,20 like football and criket ,10 like tennis and criket ,35 like tennis and ... A: You have changed the question, but the answer is the same. There is not enough information. You ... | |
| Days of the Week - Congruence | 9/9/2006 |
| Q: If you're familiar with the congruence formula to work out the day of the week, can you please help ... A: Looking at the congruence d=N+[2.6M-0.2]+ Y+[Y/4] +[C/4]-2C -(1+L)[M/11] mod 7 When we keep the ... | |
| set theory | 9/9/2006 |
| Q: there are 50 people 20 like jukebox + games, 10 like games + book , and 35 like book + juke box ... A: There does not appear to be sufficient data here to answer the question. I assume that the 35 who ... | |
| babys looks | 9/6/2006 |
| Q: i have brown hair and brown very brown eyes my father does also.my mother has blue eyes and blonde ... A: This is not really a question for a number theory expert, but I will give you an analysis based on ... | |
| euclid's algorithm | 9/5/2006 |
| Q: ok, how did u get s(x) and t(x)? d(x)=-1/10(4x+11)a(x) = 1/10(4x^2-x-1)b(x) where does ... A: I have obviously overestimated your algebraic manipulation ability. I will fill in the gaps. From ... | |
| euclid's algorithm | 9/5/2006 |
| Q: c(x)=8x^2-14x-4 The second division gives 32b(x)=(4x+11)c(x)+10d(x) I am sure you will be able to ... A: The point about the Euclidean algorithm is that it proceeds by successive divisions. To do an ... | |
| euclid's algorithm | 9/5/2006 |
| Q: you say to multiply 32b. how do i know what amount to multiply by? could i have used any multiple so ... A: A good question Daniel! If we are trying to divide x^3+.... by 8x^2+.... it is obvious we are going ... | |
| euclid's algorithm | 9/5/2006 |
| Q: find greatest common divisor of: a(x) = (x^4) -2(x^3)-(x)+2 b(x) = (x^3) + (x^2)-5(x)-2 express d(x) ... A: We are not interested in numerical factors here and we know that any gcd must be monic(leading ... | |
| Equivalence Relations | 9/4/2006 |
| Q: I understand equivalence relations but this one on my study guide threw me for a loop. Please help! ... A: I am not sure if you know the definition of an equivalence relation. About 50 years ago I learned ... | |
| Math Induction | 9/4/2006 |
| Q: On proofs like this is there a standard way to determine each step based on the setup or is each ... A: I am afraid that there is no easy answer. You just have to study different types. In the ... | |
| Math Induction | 9/4/2006 |
| Q: You answered a question I had before and I appreciate it I have an example I am working to study for ... A: This is very similar to the previous one, though you have missed out some brackets. It should read ... | |
| Mathematical Proofs | 9/4/2006 |
| Q: I am hoping I am in the right area to ask for help. I need help in setting up and proving the ... A: Yes, you are in the right area here. I hope that you are familiar with proofs by induction because ... | |
| Unity symbol | 8/16/2006 |
| Q: I am looking for a unity symbol, perhaps taken from math symbols, to use in a graphic representing a ... A: The usual meaning for the capital U is for the union of two sets, for example AUB is the notation ... | |
| Modular exponentiation | 8/11/2006 |
| Q: I am grateful that you gave an explaination to the RSA problem. But you did not give an answer to my ... A: Now I understand what you mean. Given the size of n and the fact that we dont know phi(n), I don`t ... | |
| Modular exponentiation | 8/10/2006 |
| Q: I am trying to understand the subject of modular exponenation for RSA problem, i.e. x^y mod n = z. ... A: Let me just go through the process of RSA. Two large primes p and q are selected. n=pq. n forms ... | |
| number puzzle | 8/2/2006 |
| Q: Its a question on the Mint. At the top it says add all the numbers, then it gives the three puzzles. ... A: I have already answered your question. If you have a calculator, try inputting 4+3X2. If it is a ... | |
| number puzzle | 8/2/2006 |
| Q: a puzzle is set as follows. Nineteen minus five = 4+3x2 = 6-5= then says add all ... A: I can't believe this is the full text of the puzzle. For a start there isn't a question. Is the ... | |
| chaos in number theory | 7/16/2006 |
| Q: sir, iam interested in knowing about the applicatons of chaos theory to number theory. in ... A: Matrix chaos mathematics has been used in the study of the Riemann Zeta function zeroes. See for ... | |
| perfect equations | 7/12/2006 |
| Q: I am a designer and fine artist. I have also studied Philosophy at Birkbeck college in London. As ... A: I'm busy marking exams at present so don't have time to write a thesis on this subject. However, my ... | |
| Riemann zeta function hypothesis | 7/9/2006 |
| Q: What wood be the best textbook to study this? Doing some research on it Thanks A: A lot depends on how much Mathematics you know. One that has had good reviews is Title: The Riemann ... | |
| Inverses | 7/8/2006 |
| Q: If one U.S. dollar is equal to 115.68 Japanese yen, one Japanese yen is equal to how many U.S. ... A: Let's start with an example nearer home. 100 cents = 1 dollar What's 1 cent worth in dollars. We ... | |
| theory numbers | 7/4/2006 |
| Q: We are a group of maths teachers following aproffessional course , we would be happy if you ... A: It is difficult to explain what the theory of numbers is about in a few short paragraphs. Most ... | |
| Divisibility | 7/1/2006 |
| Q: How do i prove that the product of three consecutive numbers is divisible by three? A: If the lowest number is a multiple of 3, there is nothing to prove. If it is not, it (a) leaves ... | |
| just the same!!! | 6/30/2006 |
| Q: ^^ it's me again, jaizelle...i thank you for your nice answer with my question but this time i'm ... A: I am afraid that there is no facility for including diagrams on this site, nor a facility for ... | |
| set theory | 6/29/2006 |
| Q: sir it's me again, avon...what i mean is an example of a worded problem just the same as to my ... A: Here is another one. Perhaps you could make one up yourself after studying this one. In a class of ... | |
| set thoery worded problem | 6/28/2006 |
| Q: 12 people in town have descided to form 3 clubs. Some are social than others, and the clubs are ... A: As it stands, your question doesn't make a lot of sense. I can't make out what 1/3 of the people ... | |
| example of worded problemusing set theory | 6/28/2006 |
| Q: sir may i ask for a simple example of wored problem that applies the set theory...of course i need ... A: 100 students in a college belong to at least one of the Math, Physics and Chemistry societies. 50 ... | |
| worded-problem applying set theory with set formulas | 6/26/2006 |
| Q: kindly give us an example of worded problem applying set theory with its set formulas and ... A: I cannot be sure what sort of question you want answered, but I will give an example which uses the ... | |
| maths | 6/19/2006 |
| Q: numbers 3 3 8 8 can only be used once, but the symbols + - / x can be used as many times but the ... A: If you don't have to use all the numbers it's easy. Just 3X8. If you must use all the numbers, I'm ... | |
| Complete the series etc. | 6/14/2006 |
| Q: Replace the ? with appropriate number- Q.1) 18, 14, 12, 11, ?, 10.25 Q.2) 5, 23, 113, 523, ? Q.3) ... A: Sorry I forgot to post that I would be away on holiday, and didn't get back till today. Q1. The ... | |
| find the missing number p | 6/3/2006 |
| Q: I know that you have answered this question once but i was not able to get it. Could you answer it ... A: I have just realised that allexperts does not update previous answers as often as I thought and the ... | |
| number theory:divisibility | 5/27/2006 |
| Q: The product of any three consecutive integers is divisible by 6. A: Exactly one of the 3 integers is divisible by 3. Either one or two of the integers is divisible by ... | |
| fibonacci numbers | 5/21/2006 |
| Q: i have recently watch the new film the da vinci code. In this one of the first things that comes up ... A: Yes, fibonacci numbers are a fascinating field of study. I presume you know that they are the ... | |
| Number combinations | 5/21/2006 |
| Q: I would like to know how many 5 digit number combinations you can do with 1 - 47 (i.e. 1 3 19 32 47 A: Sorry for the delay. I thought I had answered this question. Something must have gone wrong. The ... | |
| Adding & Subtracting Fractions | 5/19/2006 |
| Q: Here is myA pole 22 5/6 feet long is broken in two. One piece is 2 3/4 feet longer than the other. ... A: Using the hint, we add 2 3/4 feet to the length of the shorter. The total length is then 22 5/6 + 2 ... | |
| Number Theory | 5/11/2006 |
| Q: Given a number how do you find position in wythoff array ? A: The Zeckendorf expansion of a number is the sequence obtained by successively subtracting the ... | |
| Complex Trigonometric Functions | 4/14/2006 |
| Q: http://mathworld.wolfram.com/Sine.html http://mathworld.wolfram.com/Cosine.html ... A: You seem to be confusing z, a complex number, with its argument. z can be written in cartesian form ... | |
| An in-depth look at algebraic approximation of trignometric functions through infinite sums, and further results | 4/14/2006 |
| Q: I'm sure you're familiar with the Wallis product (if not, here's a link ... A: (a) You haven't given all the details. I would be interested to know how you differentiated your ... | |
| An in-depth look at algebraic approximation of trignometric functions through infinite sums, and further results | 4/14/2006 |
| Q: I'm sure you're familiar with the Wallis product (if not, here's a link ... A: I don't fell qualified to recommend books on calculus or algebra, but you can find plenty of good ... | |
| An in-depth look at algebraic approximation of trignometric functions through infinite sums, and further results | 4/14/2006 |
| Q: I'm sure you're familiar with the Wallis product (if not, here's a link ... A: First of all, please realise that calculus is not my area of expertise. I have checked your formula ... | |
| Fractions | 4/13/2006 |
| Q: I am having some difficulty solving the following: 2/3 of A's money increased by 4/5 of A's money ... A: Your problem is really caused by the archaic language in the problem. The word 'lacks' is not used ... | |
| Recommended Books | 4/11/2006 |
| Q: What is your opinion on recommended books about algebraic number theory and analytical number ... A: I think a lot depends on your level of expertise. If you are an undergraduate, 'A brief guide to ... | |
| group theory | 4/7/2006 |
| Q: Let H, N, and M be subgroups of a group G. Verify the following. (a) If N is normal in G then HN = ... A: Another abstract algebra question. (a) N is normal implies hN = Nh. That is the easily remembered ... | |
| Ring Theory | 4/7/2006 |
| Q: (a) Prove that the set S of rational numbers (in lowest term) with odd denominators is a subring of ... A: Once again this is not my main area of expertise. I have time to answer 2 questions and will try to ... | |
| Introduction to group theory | 4/6/2006 |
| Q: Let G be a group of cardinality pq where p and q are distinct primes. Show |Z(G)| = 1 or pq Thank ... A: I thought I had answered this question, but the answer must have gone astray. I am going to answer ... | |
| group theory | 4/4/2006 |
| Q: Let G be a group of cardinality pq, where p and q are distinct elements primes. Show |Z(G)|=1 or pq ... A: This is not really my area of expertise, but a number theorist has to know something about group ... | |
| various infinities | 3/27/2006 |
| Q: I would like to have a definition of a "curve". Given a definition, I would like to ask "Is the ... A: In Cantorean theory a curve is another example of a continuum. Just imagine it as a piece of string ... | |
| Fractions & Ratios | 3/12/2006 |
| Q: What simple solution, one not requiring algebra if possible, can be used to determine the missing ... A: It is possible for the first unknown to have any value whatsoever. This is because there are two ... | |
| roman numbers | 2/21/2006 |
| Q: what is AD MDCCCXCV in real numbers A: The Roman numeral representation of a number is just as real as the decimal system we use. M=1000, ... | |
| What are the advantages of... | 2/12/2006 |
| Q: What are the advantages of the hindu-arabic system(present decimal system)over the other ancient ... A: Western systems used physical representations for numbers. For instance, lines scribed in the sand ... | |
| Number Theory-Primes | 2/5/2006 |
| Q: 1.) if p > or equal to q> or equal to 5 and p and q are both primes, proved that 24 | p^2-q^2. 2.) ... A: It's great to find females studying number theory. A prime other than 2 or 3 can only be congruent ... | |
| Abstract Algebra - cyclic groups | 2/4/2006 |
| Q: If you have two elements from a group whose orders are relatively prime to one another, how do you ... A: Suppose to the contrary. Then there is an element a which is in both subgroups. Consider the ... | |
| fermats thm | 2/4/2006 |
| Q: will you please expl me in simple words the fermat's ittle theorem? mayur A: Fermat's "little" theorem states that if p is prime and a is prime to p, then a^(p-1) is congruent ... | |
| numbers 0 1 2 3 4 5 6 7 8 9 | 2/2/2006 |
| Q: please i would like to know 1 where are the decimal system came from, arabs, indians, others .....? ... A: I am not an expert on history of the number system, but here is a link to get you started. Clearly, ... | |
| divisibility | 2/1/2006 |
| Q: I am a 2-digit number divisible by 19. The sum of my digit is 14. What number am I and why ? A: There aren't many two digit multiples of 19. You can write them all down and pick the only one to ... | |
| Total Order | 1/20/2006 |
| Q: Several months ago I asked you a question that was outside of your field, but you provided me with a ... A: Every element of R2 is expressible as an ordered pair of real numbers. This can be put in 1-1 ... | |
| Solution For Question | 1/20/2006 |
| Q: Here is mySarah's age is 2/3 of Mary's and 3/4 of Ruth's. The sum of their ages is 46 years. How old ... A: Mary is 3/2 times Sarah's age i.e. 9 sixths of Sarah's age Ruth is 4/3 times Sarah's age i.e. 8 ... | |
| Sudoku design | 1/18/2006 |
| Q: Greeting Vijilant, How are Sudoku puzzles made? I do one on Sunday Times which is classified as very ... A: I too am a Sudoku addict, though I haven't gone into the business of designing them. I usually do ... | |
| 6-digit combination | 1/13/2006 |
| Q: I think I mean 6–number combinations, example: 12,31,45,26,10,2. Do you know of a web site where I ... A: Your print output would be at least 302558928 characters not counting line feeds and carriage ... | |
| 6-digit combination | 1/13/2006 |
| Q: How do I find every possible 6-digit combination using the numbers 0 through 50? Randy A: I'm afraid I don't understand the question. Digits are the numbers 0 to 9. If you mean how many ... | |
| Why 10? | 12/24/2005 |
| Q: Hi, please forgive me if this question appears a little silly. I have been trying to work out why ... A: The use of base ten certainly predates the arabic system we use. The Romans used X for ten, C for a ... | |
| equivalence relations | 12/17/2005 |
| Q: what is an eqivalence relation and an equivalence class? A: x is equivalent to y can be written x~y. For example, in the set of integers, if the relationship ... | |
| Fermat's Last Theorem | 12/16/2005 |
| Q: What is fremat's last theorem? When was the FLT proved? By whom? A: Fermat's Last theorem states that there are no solutions in positive integers for the equation x^n ... | |
| term paper,help needed | 12/14/2005 |
| Q: i am working on an assignment for a friend and cousin of mine on how some numbers are generated.the ... A: From the fact that the data in the two examples is identical apart from serial numbers differing by ... | |
| what a coincidence ! | 12/9/2005 |
| Q: vijilant, I thought pi was approximatly 3.14159 so why is it also used for 180 degrees ? why didn't ... A: 180 degrees is PI radians. The radian is a different measure of an angle from degrees. Suppose you ... | |
| Please analyze my theory. | 12/7/2005 |
| Q: although this not a question that is from school, I am wonder if my theory is true. When twidding ... A: I haven't got time to answer your question fully just now -I will later (1) You will never get to ... | |
| lub usage | 12/6/2005 |
| Q: i have been working on proving the following theorem, i have the write idea but just cant put it on ... A: I assume that you are using Q for the set of rational numbers. Consider the real line. Then the ... | |
| primary number | 11/30/2005 |
| Q: I am Eman btayna teacher in secandary school I want to ask you How we can find the root squre of ... A: Sorry I don't know any arabic and I don't know what you mean by a primary number. If you have a ... | |
| Thanks for the answer to my... | 11/23/2005 |
| Q: My another question is: Ismelda the witch is making a love potion. She must get the proportion of ... A: No, your reasoning is not correct because the jar does not contain pure migsweed. It is only 3/4 ... | |
| hai the question is corrected... | 11/22/2005 |
| Q: hai the question is corrected as follows: At the edge of a pond there are five great willows in ... A: Call the numbers a,b,c,d,e. Then after the moves, the numbers are a+4,b-1,c-1,d-1,e-1. For the ... | |
| At the edge of a pond there... | 11/21/2005 |
| Q: At the edge of a pond there are five great willows in whose branches there are in total less than 30 ... A: As stated, the problem is impossible. For instance, the fifth willow now has 4 less than before. ... | |
| Maths | 11/13/2005 |
| Q: Question1: Joe and his dad are digging a hole for a pond in their backyard. Joe can dig a hole 7m2 ... A: Q1: Joe can dig 1/5 of the hole in an hour and his dad can dig 1/3 of it. Together they can dig ... | |
| Math question | 11/8/2005 |
| Q: if you have the numbers 1-20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 and you have 4 ... A: You have used the word combinations, which in combinatorics means selections not counting as ... | |
| Diophantine equation y^2+d=x^3 | 11/3/2005 |
| Q: I would like to ask something about the equation y^2+d=x^3 d is a squarefree integer greater than ... A: I am afraid that this is outside my expertise, but you are on the right track with the mordell curve ... | |
| 2 induction questions | 10/29/2005 |
| Q: Let a sub k = 5 sub k-1 - 6a sub k-2 for all k >= 3, with term a1 = 3 and term a2 = 7. then a sub n ... A: This question is not really on number theory, but I will answer the first part. The equation is a ... | |
| proofs | 10/19/2005 |
| Q: The least common multiple (lcm) is a complementary concept to gcd: we say that a positive integer m ... A: Sorry for the delay. I have been very busy lately. There are lots of ways to prove these; I will ... | |
| math | 10/8/2005 |
| Q: i need help on magic squares A: You don't say what help you need. A magic square consists of a number of integers arranged in the ... | |
| Maths Trivia | 10/3/2005 |
| Q: Which five figure number can you multiply by four to give the same number in reverse order. A: This is not the sort of question I answer on a regular basis. I had to put my T!-92 programmable ... | |
| mathematical induction | 9/29/2005 |
| Q: i am not sure how to prove mathematical induction using only the propeties of natural numbers. A: I am not quite sure what you mean, but I am assuming you want to prove the inductive hypothesis. ... | |
| number theory | 9/18/2005 |
| Q: Would you mind explaining to me what a radix fraction is? Any help would be appreciated A: The term radix refers to the number base being used, so in base ten, the radix is ten. The number ... | |
| number theory | 9/16/2005 |
| Q: In my number theory class, which just started last week, we found the way to change base ten ... A: Assuming x,y and z are the digits in base b, the value of the number is n = xb^2+yb+z. If you want ... | |
| primes | 9/16/2005 |
| Q: I was asked this question , but dont know where to begin. What is the smallest prime number that can ... A: You could waste a lot of time on this question, thinking it was difficult. The sum of two cubes has ... | |
| Infinite Sum | 9/15/2005 |
| Q: and I apologize for posting in the wrong place. I have just one more question. I'm following all ... A: Even allexperts make mistakes when pushed for time, especially when out of their speciality. I did ... | |
| Infinite Sum | 9/14/2005 |
| Q: I am attempting to solve the following summation, and I am having difficulty. infinity S ... A: This isn't a number theory question but an algebra problem to prove a result in ... | |
| 0.99999999... = 1 (is it true=? If so help me explain this) | 9/8/2005 |
| Q: A math teacher once told me that 0.99999...=1 because 1/9=0.11111..., 2/9=0.22222... and so on, so ... A: Sorry for the delayed response, but we were away for a few days and I forgot to log it as a holiday. ... | |
| Math Theory | 8/22/2005 |
| Q: : Best wishes to the team and family that you interact with. I posted a question on August 16 of ... A: I'm not quite sure what the difficulty is now, but I repeat the calculation: S = 0.1111111... ... | |
| Math | 8/16/2005 |
| Q: How do i prove that, while 1 over .1 is equal 10, 1 over repeated points ...1 is equal 9, in other ... A: Hola Francisco There are still eminent mathematicians who dispute whether a sum to infinity can ... | |
| unique factorisation in Z[-1/2+/-sqrt(-19)/2] | 8/8/2005 |
| Q: it is well known that Z[-1/2+sqrt(19)*i/2,-1/2-sqrt(19)*i/2] (thus the algebraic integer ring in ... A: The term norm applies to any quadratic field and is useful because it helps with factorisation since ... | |
| 1/2 X 8 & 1/2 = ?/8 | 8/5/2005 |
| Q: How does or why does the answer to the following calculation equal the missing term to the ... A: One of the important ideas in solving equations is that if two quantities are equal, they are still ... | |
| Divisibility by 7 and 13 | 8/1/2005 |
| Q: I have created an original method to determine if a number is divisible by 7 and 13 that is ... A: Buenas tardes Silvio I have had a good look at your site and you have answered my previous comments ... | |
| Euclidean Algorithm | 7/19/2005 |
| Q: I have been stumped on a proof now for a week. I'm trying to prove the Euclidean Algorithm by ... A: You have assumed that gcd(a,b) = gcd(b,r). This is an easy proof, but is a necessary part of a ... | |
| Solve For ? | 7/15/2005 |
| Q: How is the following calculation solved? 2 X 3 X ? = 4 X ? ? equals the same number.) In algebra ... A: Many great songs and poems seem to be attributed to anon, so I might be communicating with somebody ... | |
| Table with four vars | 7/9/2005 |
| Q: Sorry, I didn't explain it well enough =) Actually the table is just a representation of what I want ... A: You must understand that this is not a number theory question. You could try using one of the free ... | |
| Table with four vars | 7/9/2005 |
| Q: I have a table with four variables (X1, Y1, X2, Y2), and 25 different values for each. (This is ... A: You don't tell me how the table is stored. Is it a 2-dimensional array, or is it stored in cells in ... | |
| a computer programme | 7/4/2005 |
| Q: there is a short simple programme of only a few lines long,i think it might be called the [life ... A: I just remembered I have a program on my computer called life. It is one of a suite of programs ... | |
| Patterns In Prime Numbers | 7/3/2005 |
| Q: I was reading "Archimedes' Revenge" which states that a simple formula that generates all prime ... A: I'm afraid there is still no simple formula for generating all prime numbers, nor is there a quick ... | |
| Proofs | 6/24/2005 |
| Q: if a^(n)-1 is a prime...1)prove that a=2 and 2)that n = prime? I proved the first part,but am ... A: I'll answer your first question and hope to get back to you with the second. You have made a good ... | |
| Birthday paradox | 6/8/2005 |
| Q: What is the probability that at least two people from 24 people have the same birthday? (Assume 365 ... A: We calculate the probability of the birthdays all being different. The number of ways to allocate 24 ... | |
| Learning independently | 6/7/2005 |
| Q: I just graduated from highschool. I am going into the field of Math at college. I am not sure if I ... A: You are a winner. You have triumphed over your adversity and succeeded. I am sure you will ... | |
| Prime Numbers | 5/24/2005 |
| Q: I am trying to find out how to work out how many prime numbers there are between 1 and a million. ... A: There is definitely no quick and easy way. You have to count them or look up the answer in a book. ... | |
| Theta(x), related to primes, zeta fn etc. | 5/20/2005 |
| Q: Let Theta(x) = SUM (of primes less than or equal to x) Log p Prove theta(x) <= (log 4)x A: The following is a standard theorem on prime number distribution. See for instance Theorem 8.5 in ... | |
| pi, phi, square roots, and infinite decimals | 5/19/2005 |
| Q: I have recently become infatuaded with these long numbers, and have scoured the web. Now I have my ... A: What a lot of questions. There is no real point in computing constants like PI to many places of ... | |
| Squaring | 5/19/2005 |
| Q: Sorry if this is in the wrong area or dumb or anything. I'm wondering how you could square a large, ... A: There is no generally quick method for squaring a large number, but if it has some special form, as ... | |
| general math | 5/18/2005 |
| Q: May I know what's the difference between pure and applied math? I even heard there's a third type, ... A: Pure mathematics is the study of numbers purely for their own sake. So algebra, geometry, ... | |
| not really a question.. about FLT | 5/14/2005 |
| Q: this is not really a question.. you might be interested in what the link below has to say on Wiles' ... A: I think the date of this article should have been April 1st. It rather reminds me of an article ... | |
| Number Theory Proof | 5/12/2005 |
| Q: solve system of linear congruences using chinese remainder theorem. x= 2(mod7) x= 5(mod6) x= 0(mod5) ... A: The inverse of 6*5=30 mod 7 is 4. 4*30=1 mod 7 The inverse of 5*7=35 mod 6 is 5 The inverse of ... | |
| Number Theory Proof | 5/12/2005 |
| Q: Can you help me answer and prove the following question please? What is the remainder when 5^6002 ... A: Are you familiar with Fermat's theorem? a^(p-1) is congruent to 1 mod p if p is prime and a is not a ... | |
| arithmetic problems and number series | 5/9/2005 |
| Q: I'd appreciate if you could recommend any internet resources that's help me get ready for a test ... A: You are unfortunately in a system where they can't afford to pay exam markers properly, so they have ... | |
| primes | 5/4/2005 |
| Q: I have read about prime numbers but nothing has ever prepared me for this question. Please help. ... A: This is very similar to Polignac's conjecture(1848),except he claimed all odd numbers could be ... | |
| divisibility | 5/4/2005 |
| Q: I am not getting a gripe on these kind of problems I need help please. Find all pairs of positive ... A: First note that a and b must both be odd since b^2+b is even. I think this problem is like a chain. ... | |
| Chinese Remainder Theorem | 5/4/2005 |
| Q: Hallo. Hope you are doing fine. I've been unwell thats why you haven't heard from me. I need help ... A: If you were solving the algebra equation 5x=12, you could do it by multiplying both sides by the ... | |
| powers and mod | 4/23/2005 |
| Q: Find the last five digits of the number 9^(9^(9....(9^(9^(9^9)))...)) for 1001 9's. ie 1001 ... A: I couldn't find a way to do this analytically. I wrote a program for my TI-92 calculator and it came ... | |
| non-axiomatic thought system | 4/22/2005 |
| Q: Please try to answer my question : is there any logical reason for mathematical problems like, ... A: We don't have to measure Pi, we can calculate it. But our calculations are based on Euclidean ... | |
| positive integers | 4/21/2005 |
| Q: My name is Alice, a Math teacher. I challenge my mind once in a while and I got this question that ... A: No 3 successive terms are equal, so each product is either aab or abb. Each term appears 3 times in ... | |
| Odd number out question causing headache | 4/21/2005 |
| Q: I've been given the following number sequence puzzle by a family friend who writes the things for a ... A: This is a strange one. The encyclopaedia of integer sequences at ... | |
| Mathmetics | 4/20/2005 |
| Q: Please help my daugther with the easiest way to get this answer. Thanks N + 6 = 22 - N N = A: To solve simple equations we carry out the same mathematical operation on both sides. The operation ... | |
| orthogonal subspaces | 4/16/2005 |
| Q: I know this isn't quite Number Theory, but was wondering if you could help me with this question? ... A: This isn't my field and I gave my books on vector spaces to an impoverished student, but I am pretty ... | |
| GCF, LCM | 4/15/2005 |
| Q: When you say co- prime, does that mean that there is no GCF or LCM because-23 is a prime number and ... A: Yes. You've hit the nail on the head. When numbers are co-prime it means the greatest common ... | |
| number theory | 4/14/2005 |
| Q: Here is anotherLet d and n be integers greater than 1 such that d|n. Suppose that a is a primitive ... A: Gauss showed that the only numbers with primitive roots are 2,4,p^k and 2*p^k. The proof of this is ... | |
| consecutive numbers | 4/14/2005 |
| Q: Let f:N\{0,1} ~N be a function defined by: f(n)=lcm[1,2,...,n] Prove that for all n,n>=2, there ... A: I don't understand what the f:N\{0,1}~N means. I think you are on the right track thinking about ... | |
| Divisibility by seven | 4/13/2005 |
| Q: Please enter www.divisibilitybyseven.mat.br to take notice about a new divisibility by seven rule A: I am now convinced that your method does work, but doesn't involve less mathematical operations than ... | |
| Number Theory! | 4/11/2005 |
| Q: Find all integers n, which are divisible by all the integers less than square root of n. Prove these ... A: Let's try to find the next one. 25 is no good, and numbers above 25 need a factor 5. But it ... | |
| Brief method for determining if a number is a multiple of 7 | 4/11/2005 |
| Q: I am not a Mc Auley student This article was already sent to the national library of Brazil, and ... A: I am not convinced that it is superior to the method I sent you and is not as straightforward as ... | |
| multiplicative orders | 4/11/2005 |
| Q: I was very close to the answer I just needed someone to direct my thoughts in the right direction. ... A: In the follow up, the number a doesn't have to be a primitive root, i.e. one such that ... | |
| multiplicative orders | 4/10/2005 |
| Q: Can you please help me with this question? Suppose d and n are integers greater than 1 such that ... A: The integers less than n and prime to it, which include a or an integer a'congruent to a mod n, form ... | |
| complex math | 4/9/2005 |
| Q: There's a math problem I've been struggling with for several years and I was wondering if you could ... A: Sorry I can't help you a lot over this. It isn't really my field, but I did teach a course a few ... | |
| perfect numbers | 4/9/2005 |
| Q: independent study: hope you are having a restful weekend. I wish to request you to help me ... A: To do this question, you need to understand first of all, how to calculate the sigma function ... | |
| Fermat's Last Theorem | 4/1/2005 |
| Q: I am doing a calculus project on Sophie Germain. I have to write about a piece of mathematics that ... A: I don't think her number theory work has anything to do with calculus, but her work on elasticity ... | |
| Number of Ways | 3/31/2005 |
| Q: I wonder if you can help with this one. (Hope my explanation makes sense!) I pick 11 different ... A: This is not a number theory question but a combinatorics one. However, since I have no teaching to ... | |
| what does it mean that whole... | 3/28/2005 |
| Q: what does it mean that whole numbers are closed under addition but not under subtraction? A: By whole numbers I presume you mean the natural numbers 1,2,3.... Whenever you add two of these ... | |
| limits | 3/25/2005 |
| Q: I have just purchased the book,Calculus for Dummies,and I found that by limits, it doesn't teach ... A: There are a number of ways to do this. One way is to write an infinite series for 2^x and divide it ... | |
| divisibility by 7 | 3/18/2005 |
| Q: I created a method to determine the divisibility of a number by 7, no matter the extension of the ... A: You are clearly a creative person and proud of your achievement. Your method may be a variation of ... | |
| worded problem | 3/17/2005 |
| Q: in a group of 120 movie critics, 70 do not like Fellini, 90 like Tarkovsky, and 21 do not like both. ... A: This is a simple example is set theory. 50 like F and 90 like T. 120-21 = 99 like either or both. ... | |
| Fibonacci question | 3/17/2005 |
| Q: I am stuck on the following problem and have no idea how to solve it. I would appreciate your help. ... A: I assume you know what is needed in a proof by induction. We need to show that the statement is true ... | |
| Maths Puzzle | 3/10/2005 |
| Q: Can you answer this question " 999,999 to the power of 1,000,000 is a number of almost 6 million ... A: This question is about modular arithmetic. Two numbers are congruent to each other mod n if they ... | |
| math | 3/9/2005 |
| Q: I was doing these binominal probabability distribution questions and i'm stuck on a few of them. ... A: You should be able to do most of these using the method I showed you. Q1. Work out the probability ... | |
| math | 3/9/2005 |
| Q: a sales person has to sell a minimum of 50 cars in a month in order to get a bonus . one particular ... A: This is a statistics question and is a simple example of the Binomial distribution. The number of ... | |
| Inverting Fractions | 3/2/2005 |
| Q: I am curious to know whether or not it is possible to invert a mixed number such as 3 1/2 without ... A: You are an investigator. You have tried to seek a method. Good. You found out that inversion ... | |
| irrational numbers | 2/28/2005 |
| Q: Although irrational numbers are infinite nonrepeating decimals and cannot therefore be "written ... A: An expressible number means that you can describe the number by a finite string of characters. The ... | |
| divisibility | 2/26/2005 |
| Q: why 0/0 can't be defined A: Consider the following three expressions. (a) sin(x)/x (b) sin(x)/(x^2) (c) sin(x)/(x^(1/2)) If we ... | |
| From Pounds To Ounces | 2/7/2005 |
| Q: I want to thank you for the reply. I have a follow-up question or two. 1. Yes or No - Does the ... A: 1. Yes you have to find the number of ounces in one quarter of a pound. This is testing if you know ... | |
| number line | 1/24/2005 |
| Q: I hope I am posting this question where it's appropriate.On the number line, 1.4 is halfway between ... A: You need to work out the mid-point for each answer. To get the mid-point you add the numbers and ... | |
| square roots | 1/14/2005 |
| Q: What is the step by step process for calculating the square root of a given number? A: I'll do an example. However, the digits won't line up properly. The commas should be underneath one ... | |
| unit fractions | 1/10/2005 |
| Q: what are the three unit fractions that sums up to give 1? tell me the process plz. A: I presume you mean three different unit fractions. Clearly it is easy if they do not have to be ... | |
| Euclidean Algorithm | 1/4/2005 |
| Q: I want to thank you for your reply. However, I need some clarification. 1. I am not familiar with ... A: The process of subtracting multiples of the smallest number is just the same as taking the remainder ... | |
| Euclidean Algorithm | 1/3/2005 |
| Q: Can the Euclidean Algorithm be used on more than two numbers to determine the greatest common ... A: There is no limit to the number of numbers. I'll choose a better example to show how it works. 16, ... | |
| ~HELP PLEASE~ | 12/18/2004 |
| Q: Noah Ate Peas. Same letters stand for the same digits. Different letters stand for different digits. ... A: I don't normally answer puzzles of this sort, but I had a few minutes to spare, so here you are. ... | |
| Well, I read in a low profile... | 12/16/2004 |
| Q: Well, I read in a low profile dictionary entry that the definable numbers can be counted (that is, ... A: This question can be answered by the classic Cantor argument. Suppose you have enumerated all ... | |
| Proportions | 12/15/2004 |
| Q: Yes, I made an error the proportion should be 2/4 = ?/8. I know about the shortcut method, cross ... A: Let's use some algebra so that special relationships between numbers which exist in the example (all ... | |
| Hi, What is the best you... | 12/15/2004 |
| Q: What is the best you can do when it comes to enumerating all possible mappings between sets of ... A: I am now in a position to give an authoritative answer to your question. My first response was out ... | |
| Recursion | 12/15/2004 |
| Q: Not a McAuley student. A walkway is to be paved with a row of square tiles with 3 colors: red, ... A: This is an interesting question I haven't seen before. If we have a walkway of n-1 tiles and wish to ... | |
| number theory | 12/12/2004 |
| Q: Is a number a multiple of itself? A: Yes. The definition of multiple of an integer is that integer multiplied by an integer including 1. ... | |
| Fi number | 12/7/2004 |
| Q: I'm 19 year-old student of applied mathematics from Poland. My problem is that I can't cope with a ... A: You must be familiar with phi and know that the quadratic equation that defines it is f^2 = f + 1. I ... | |
| Proportions | 12/6/2004 |
| Q: I want to thank you for the reply. I can do the mathematics, but I do not fully understand why it ... A: I appreciate that I may have used some big words which you didn't understand. You do know that when ... | |
| Proportions | 12/5/2004 |
| Q: I know that this question my be outside of your expertise, but I hope that you can provide a reply. ... A: Remember that multiplying or dividing both elements of a proportion or both numerator and ... | |
| please help*** | 12/4/2004 |
| Q: can you please help me with the question below: thnx. Use each of these digits just once: ... A: The 5 is the first one to fix, since it cannot be a units digit. It must be the tens digit in the ... | |
| find nth digit of 0.1234567891011... | 12/4/2004 |
| Q: Please try to explain the algorithm, in words or in a program, basic or c, as simply as possible. ... A: First we find a formula for the number of digits used to write all the numbers of up to n ... | |
| find nth digit of 0.1234567891011... | 12/1/2004 |
| Q: I would like to know a fast way to find the nth digit of 0.1234567891011... without having to count ... A: I've been working on it. It depends what you mean by fast. I worked out that the 10^100th digit is ... | |
| the number 'e' | 11/27/2004 |
| Q: This is my third and last question on subject. It is reported that Euler exclaimed, "God exists!", ... A: Euler's formula is e^(i*PI) + 1 =0. Incredible. All 5 of the most important mathematical numbers in ... | |
| the number 'e' | 11/26/2004 |
| Q: appreciate your explanation of e in terms of continuously compounding interest; i.e., continuous ... A: A function that has the variable as a power or exponent is called an exponential function. The one ... | |
| evaluating using prime factors | 11/21/2004 |
| Q: i am stuck on this question and I would very much appreciate your help, unfortunately i can't type ... A: First you need to find the prime factors. There are many methods, but the easiest one for me to ... | |
| the number 'e' | 11/9/2004 |
| Q: Can you refer me to a layman's explanation of the number 'e'. Can such an explanation even exist? ... A: It depends what you mean by a layman. I will assume the layman has no knowledge of calculus but ... | |
Vijilant
Top Expert on this page
Expertise
Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.
Experience
Teacher of math for 50 years
Organizations
ATL
Publications
Journal of mathematics and its applications
Education/Credentials
BSc Hons Liverpool
Awards and Honors
State Scholarship 1955
Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things.
One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.
©2012 About.com, a part of The New York Times Company. All rights reserved.