# Problem 407: Idempotents
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.