Let $p$ be a prime and $\mathbb Z/p\mathbb Z[x] $ be the set of polynomials with coefficients in $\mathbb Z /p\mathbb Z $ What can you say about the roots of the polynomial $x^{p-1} -[1] \in \mathbb Z / p \mathbb Z$.
I know that if $[a] \in \mathbb Z / p \mathbb Z$ then the root of a polynomial say $g \ \in \mathbb Z / p \mathbb Z$ is: $g([a]) = [0]. $
Can anyone provide some guidance am I suppose to use fermat's little theorem to deduce something?