Which condition is necessary for x2+y2=nx^2 + y^2 = nx2+y2=n to be solvable in integers?
nnn must be prime
All prime factors of nnn of the form 4k+34k+34k+3 must have an even exponent
All prime factors of nnn of the form 4k+14k+14k+1 must have an even exponent
nnn must be a perfect square