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## Homework Statement

Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.)

## Homework Equations

## 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?