1. The problem statement, all variables and given/known data Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.) 2. Relevant equations 3. The attempt at a solution a^2+b^2=4n+3=3 mod 4 is impossible if you look at the possibilities of a^2 and b^2. I did not use the fact that the number is prime. Am I missing something?