maniac wrote:
If p, m, and n are positive integers, n is odd, and p = m^2 + n^2, is m divisible by 4?
(1) When p is divided by 8, the remainder is 5.
(2) m – n = 3
A.
1) p = 8k+5
so p is odd.
also, p = m^2 + n^2
n is odd so for p to be odd m needs to be even.
1^2 mod 8 = 1
2^2 mod 8 = 4
3^2 mod 8 = 1
4^2 mod 8 = 0
and then it repeats.
we know (m^2 + n^2) mod 8 = 5 ; where m is even and n is odd
in the range given above m can be 2 and n can be either 1 or 3
m and n both have a cyclicity of 4 -->
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