Separability of a cyclotomic polynomial modulo p
= Separability of a cyclotomic polynomial modulo p
{c}
If the prime $p$ does not divide $n$, then $X^n-1$ is square-free over $\mathbb F_p$ because its derivative $nX^{n-1}$ is coprime to it. Its factor $\Phi_n$ is therefore separable modulo $p$.