Pythagorean primes

Fermat stated that an odd prime p can be expressed as a sum of two squares if and only if p leaves a remainder of 1 when divided by 4:

p = a² + b² ⇔ p ≡ 1 (mod 4),

where a and b are some positive integers.  Such primes are called Pythagorean primes.

If you are interested, the proof can be found in any elementary number theory textbooks.