---
id: 5900f4711000cf542c50ff84
challengeType: 5
title: 'Problem 261: Pivotal Square Sums'
forumTopicId: 301910
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler261()</code> should return 238890850232021.
    testString: assert.strictEqual(euler261(), 238890850232021);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler261() {

  return true;
}

euler261();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>