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

id, challengeType, title, forumTopicId

id	challengeType	title	forumTopicId
5900f5041000cf542c510016	5	Problem 407: Idempotents	302075

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

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

Challenge Seed

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

euler407();

Solution

// solution required