Fermat's theorem on sums of two squares

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2},} with x and y integers, if and only if p ≡ 1 ( mod 4 ) . {\displaystyle p\equiv 1{\pmod {4}}.} The prime numbers for which this is true are called Pythagorean primes.