<Dl> <Dd> p ≡ 1 (mod 4). (\ displaystyle p \ equiv 1 (\ pmod (4)).) </Dd> </Dl> <Dd> p ≡ 1 (mod 4). (\ displaystyle p \ equiv 1 (\ pmod (4)).) </Dd> <P> The prime numbers for which this is true are called Pythagorean primes . For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways: </P> <Dl> <Dd> 5 = 1 2 + 2 2, 13 = 2 2 + 3 2, 17 = 1 2 + 4 2, 29 = 2 2 + 5 2, 37 = 1 2 + 6 2, 41 = 4 2 + 5 2 . (\ displaystyle 5 = 1 ^ (2) + 2 ^ (2), \ quad 13 = 2 ^ (2) + 3 ^ (2), \ quad 17 = 1 ^ (2) + 4 ^ (2), \ quad 29 = 2 ^ (2) + 5 ^ (2), \ quad 37 = 1 ^ (2) + 6 ^ (2), \ quad 41 = 4 ^ (2) + 5 ^ (2).) </Dd> </Dl>

Numbers that are the sum of two squares