---
id: 5900f3e41000cf542c50fef7
challengeType: 5
title: 'Problem 120: Square remainders'
---
## Description
Let r be the remainder when (a−1)n + (a+1)n is divided by a2.
For example, if a = 7 and n = 3, then r = 42: 63 + 83 = 728 ≡ 42 mod 49. And as n varies, so too will r, but for a = 7 it turns out that rmax = 42.
For 3 ≤ a ≤ 1000, find ∑ rmax.
## Instructions
## Tests
```yml
tests:
- text: euler120() should return 333082500.
testString: assert.strictEqual(euler120(), 333082500, 'euler120() should return 333082500.');
```
## Challenge Seed
```js
function euler120() {
// Good luck!
return true;
}
euler120();
```