yaworsw/euler-manager

---
:id: 273
:name: Sum of Squares
:url: https://projecteuler.net/problem=273
:content: |+
  Consider equations of the form: <var>a</var><sup>2</sup> + <var>b</var><sup>2</sup> = <var>N</var>, 0 ≤ <var>a</var> ≤ <var>b</var>, <var>a</var>, <var>b</var> and <var>N</var> integer.

  For <var>N</var>=65 there are two solutions:

  <var>a</var>=1, <var>b</var>=8 and <var>a</var>=4, <var>b</var>=7.

  We call S(<var>N</var>) the sum of the values of <var>a</var> of all solutions of <var>a</var><sup>2</sup> + <var>b</var><sup>2</sup> = <var>N</var>, 0 ≤ <var>a</var> ≤ <var>b</var>, <var>a</var>, <var>b</var> and <var>N</var> integer.

  Thus S(65) = 1 + 4 = 5.

  Find ∑S(<var>N</var>), for all squarefree <var>N</var> only divisible by primes of the form 4<var>k</var>+1 with 4<var>k</var>+1 \< 150.