I have to prove the following question:
Show that for any prime $p$ and any polynomial $a_0 + a_1 \cdot X + \ldots + a_{n-1} \cdot X^{n-1} + a_n \cdot X^n$ in $\mathbb{Z}/p\mathbb{Z}[X]$, we have
$$(a_0 + a_1 \cdot X + \ldots + a_{n-1} \cdot X^{n-1} + a_n \cdot X^n)^p \\= a_0 + a_1 \cdot X^p + \ldots + a_{n-1} \cdot X^{p\cdot (n-1)} + a_n \cdot X^{p\cdot n}$$
I have no idea on how to start, any hints?
