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.

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter