# Problem 273: Sum of Squares

![graphic](img273.gif)

Consider equations of the form: a2 + b2 = N, 0 ≤ a ≤ b, a, b and N
integer. For N=65 there are two solutions: a=1, b=8 and a=4, b=7. We
call S(N) the sum of the values of a of all solutions of a2 + b2 = N, 0
≤ a ≤ b, a, b and N integer. Thus S(65) = 1 + 4 = 5. Find ∑S(N), for all
squarefree N only divisible by primes of the form 4k+1 with 4k+1 <
150.