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

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

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler120()</code> should return 333082500.
    testString: assert.strictEqual(euler120(), 333082500);

```

</section>

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

<div id='js-seed'>

```js
function euler120() {

  return true;
}

euler120();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>