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.

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http://projecteuler.net/problem=407