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Sum of Squares

Problem 273

Published on Saturday, 9th January 2010, 01:00 pm; Solved by 832

Consider equations of the form: a2 + b2 = N, 0 ≤ ab, 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 ≤ ab, 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.