## Idempotents

### Problem 407

Published on 23 December 2012 at 10:00 am [Server Time]

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.