Part a) Let a be an odd integer. Prove that a^2 is congruent to 1 mod 8. Deduce that a^2 is congruent to 1mod4.

Part b) Prove that if n is a positive integer such that n is congruent to 3mod4, then n cannot be written as the sum of two squares of integers.

Prove or disprove the converse of part b)