# Proof

If $$a$$ is an integer, $$p$$ is a prime number, and $$a$$ is not divisible by $$p,$$ then $$a^{p - 1} \equiv 1 \pmod{p}$$
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If $$a$$ is an integer, $$p$$ is a prime number, and $$a$$ is not divisible by $$p,$$ then $$a^p \equiv a \pmod{p}$$