We know
$a^p \equiv a \pmod p\quad p\text{ a prime, }0\leq a \leq p-1.$
But if we have $b$, not prime, what's the new formula? $a^b \equiv\ ? \pmod b,\quad b\text{ not a prime, } 0\leq a \leq b-1\ $
How to find it?
OBS.: To someone who has reputation enough, I think it's interesting create a new tag named composite-numbers.