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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-407-idempotents.md

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+---
+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 < 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
+```