Advanced Math/Proofs

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Expert: Robi Bhattacharjee - 11/10/2008


Question
Let a and b be elements of the set of integers. Prove that if a^2+b^2 is equivalent to 0(mod3), then either a and b are both congruent to 0 modulo 3 or neither is congruent to O modulo 3.

Answer
Hi Pete,

Well, basically we have to prove that it is impossible to have a congruent to 0 while b isn't.

So a^2 + b^2 = b^2 mod(3)

because a^2 = 0 mod(3)

so this means that b^2 must = 0 mod 3 but it doesn't therefore it is impossible for a to be 0 while b isn't.

So therefore the statement is true.


I hope this helped,
Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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