43 lines
907 B
Markdown
43 lines
907 B
Markdown
|
---
|
||
|
|
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
|
||
|
|
```
|