yaworsw/euler-manager

---
:id: 261
:name: Pivotal Square Sums
:url: https://projecteuler.net/problem=261
:content: |+
  Let us call a positive integer <var>k</var> a <var>square-pivot</var>, if there is a pair of integers <var>m</var> \> 0 and <var>n</var> ≥ <var>k</var>, such that the sum of the (<var>m</var>+1) consecutive squares up to <var>k</var> equals the sum of the <var>m</var> consecutive squares from (<var>n</var>+1) on:

  (<var>k</var>-<var>m</var>)<sup>2</sup> + ... + <var>k</var><sup>2</sup> = (<var>n</var>+1)<sup>2</sup> + ... + (<var>n</var>+<var>m</var>)<sup>2</sup>.

  Some small square-pivots are

  - **4** : 3<sup>2</sup> + **4** <sup>2</sup> = 5<sup>2</sup>
  - **21** : 20<sup>2</sup> + **21** <sup>2</sup> = 29<sup>2</sup>
  - **24** : 21<sup>2</sup> + 22<sup>2</sup> + 23<sup>2</sup> + **24** <sup>2</sup> = 25<sup>2</sup> + 26<sup>2</sup> + 27<sup>2</sup>
  - **110** : 108<sup>2</sup> + 109<sup>2</sup> + **110** <sup>2</sup> = 133<sup>2</sup> + 134<sup>2</sup>

  Find the sum of all **distinct** square-pivots ≤ 10<sup>10</sup>.