Some context - knowing if a number can be written as a sum of squares can be reduced to determining whether its factors can be written as a sum of squares (proo

Some context - knowing if a number can be written as a sum of squares can be reduced to determining whether its factors can be written as a sum of squares (proof of this involves the fact that norm of complex numbers respects multiplication). So the prime case becomes important. 4n+3 type primes cant be written as squares are either 0 or 1 modulo 4. 2 can be written. Which leaves the 4n+1 prime case which is fermats theorem.