---
id: 5900f4711000cf542c50ff84
challengeType: 5
title: 'Problem 261: Pivotal Square Sums'
---
## Description
Let us call a positive integer k a square-pivot, if there is a pair of integers m > 0 and n ≥ k, such that the sum of the (m+1) consecutive squares up to k equals the sum of the m consecutive squares from (n+1) on:
(k-m)2 + ... + k2 = (n+1)2 + ... + (n+m)2.
Some small square-pivots are
4: 32 + 42
= 52
21: 202 + 212 = 292
24: 212 + 222 + 232 + 242 = 252 + 262 + 272
110: 1082 + 1092 + 1102 = 1332 + 1342Find the sum of all distinct square-pivots ≤ 1010.
## Instructions
## Tests
```yml
tests:
- text: euler261() should return 238890850232021.
testString: assert.strictEqual(euler261(), 238890850232021, 'euler261() should return 238890850232021.');
```
## Challenge Seed
```js
function euler261() {
// Good luck!
return true;
}
euler261();
```