---
id: 5900f5041000cf542c510016
challengeType: 5
title: '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 < n such that a2 ≡ a (mod n).
So M(6) = 4.
Find ∑M(n) for 1 ≤ n ≤ 107.
## Instructions
## Tests
```yml
tests:
- text: euler407() should return 39782849136421.
testString: assert.strictEqual(euler407(), 39782849136421, 'euler407() should return 39782849136421.');
```
## Challenge Seed
```js
function euler407() {
// Good luck!
return true;
}
euler407();
```