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

# --hints--

`euler261()` should return 238890850232021.

```js
assert.strictEqual(euler261(), 238890850232021);
```

# --seed--

## --seed-contents--

```js
function euler261() {

  return true;
}

euler261();
```

# --solutions--

```js
// solution required
```