Problem 407

Idempotents

If we calculate `a`^{2} mod 6 for 0 `a` 5 we get: 0,1,4,3,4,1.

The largest value of `a` such that `a`^{2}`a` mod 6 is 4.

Let's call M(`n`) the largest value of `a` `n` such that `a`^{2}`a` (mod `n`).

So M(6) = 4.

Find M(`n`) for 1 `n` 10^{7}.

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