Question 101
Let $m, n \geqslant 2$ be integers verifying the following property: $$
a^{n} \equiv 1 \quad(\bmod m) \quad a=1, \ldots, n
$$ Prove that $m$ is a prime number and $n = m - 1$.
a^{n} \equiv 1 \quad(\bmod m) \quad a=1, \ldots, n
$$ Prove that $m$ is a prime number and $n = m - 1$.