simple one, after you get to know about the Fermat’s Theorem…. and also if
n = 4*k + 3, it can never be a sum of two squares.
even^2 + even^2 = 4*k
odd^2 + even^2 = 4*k + 1
odd^2 + odd^2 = 4*k + 2
Fermat’s Theorem: A number n is a sum of two squares if and only if all prime factors of n of the form 4m+3 have even exponent in the prime fatorization of n.