---
id: 5900f3e41000cf542c50fef7
title: 'Problem 120: Square remainders'
challengeType: 5
forumTopicId: 301747
dashedName: 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.

# --hints--

`euler120()` should return 333082500.

```js
assert.strictEqual(euler120(), 333082500);
```

# --seed--

## --seed-contents--

```js
function euler120() {

  return true;
}

euler120();
```

# --solutions--

```js
// solution required
```
