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2021-02-06 04:42:36 +00:00
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curriculum/challenges/chinese/10-coding-interview-prep/project-euler/problem-407-idempotents.md
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---
id: 5900f5041000cf542c510016
title: 问题407：幂等元素
title: 'Problem 407: Idempotents'
challengeType: 5
videoUrl: ''
forumTopicId: 302075
dashedName: problem-407-idempotents
---
# --description--
如果我们计算a2 mod 6为0≤a≤5，我们得到：0,1,4,3,4,1。
If we calculate a2 mod 6 for 0 ≤ a ≤ 5 we get: 0,1,4,3,4,1.
a2≡amod 6的最大值为4.让我们将M（n）称为a <n的最大值，使得a2≡a（mod n）。所以M（6）= 4。
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.
找ΣM（n）为1≤n≤107。
Find ∑M(n) for 1 ≤ n ≤ 107.
# --hints--
`euler407()`应该返回39782849136421。
`euler407()` should return 39782849136421.
```js
assert.strictEqual(euler407(), 39782849136421);