I must prove the theorem that if the GCD of a and b is 1, and if p is an odd prime which divides a^2 + b^2, p is of the form 4n + 1.
I have seen two proofs that I think might be helpful.
1. If a and b are relatively prime then every factor of a^2 + b^2 is a sum of two squares.
2. Every prime of the form 4n + 1 is a sum of two squares.
I got these from:
The Attempt at a Solution
I realize now that if I can prove that a prime of the form 4n + 3 cannot be written as the sum of two primes, then I can prove the original theorem. I'm not sure if this is true, however, or how to prove it if it is. If it is not true, I have no idea where to start looking for help. Does anybody have an idea?