---
id: 5900f5041000cf542c510016
title: 'Problem 407: Idempotents'
challengeType: 5
forumTopicId: 302075
dashedName: problem-407-idempotents
---

# --description--

If we calculate a2 mod 6 for 0 ≤ a ≤ 5 we get: 0,1,4,3,4,1.

The largest value of a such that a2 ≡ a mod 6 is 4. Let's call M(n) the largest value of a &lt; n such that a2 ≡ a (mod n). So M(6) = 4.

Find ∑M(n) for 1 ≤ n ≤ 107.

# --hints--

`euler407()` should return 39782849136421.

```js
assert.strictEqual(euler407(), 39782849136421);
```

# --seed--

## --seed-contents--

```js
function euler407() {

  return true;
}

euler407();
```

# --solutions--

```js
// solution required
```
