freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-407-idempotents.english.md

---
id: 5900f5041000cf542c510016
challengeType: 5
title: 'Problem 407: Idempotents'
---

## Description
<section id='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 < n such that a2 ≡ a (mod n).
So M(6) = 4.


Find ∑M(n) for 1 ≤ n ≤ 107.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler407()</code> should return 39782849136421.
    testString: assert.strictEqual(euler407(), 39782849136421, '<code>euler407()</code> should return 39782849136421.');

```

</section>

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

<div id='js-seed'>

```js
function euler407() {
  // Good luck!
  return true;
}

euler407();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>