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Hello Janet,

Can you help me solve this question:

Q: lf (3x)/8 has a remainder of 4 and (3y)/8 has a remainder of 2 then (xy)/8 has a remainder of_______

the answer is 0

Thanks

Thi

3x mod8 = 4, so there is an integer m such that

3x = 8m + 4

= 4(m + 1)

4(m + 1) is divisible by 3.

Since 4 is not divisible by 3, (m + 1)/3 must be an integer.

Therefore, x is divisible by 4.

3y mod8 = 2, so there is an integer n such that

3y = 8n + 2

= 2(4n + 1)

2(4n + 1) is divisible by 3.

Since 2 is not divisible by 3, (4n + 1)/3 must be an integer.

Therefore, y is divisible by 2.

xy is divisible by 4·2 = 8, so xy mod8 = 0

xy/8 has a remainder of 0.

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