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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.

1 Answers 1