## Sum of Squares

### Problem 273

Published on Saturday, 9th January 2010, 01:00 pm; Solved by 769

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.