Artin–Schreier polynomial
= Artin–Schreier polynomial
{c}
An Artin–Schreier polynomial over a field of characteristic $p$ has the form
$$
X^p-X-a.
$$
If it has one root $\alpha$, all its roots are $\alpha+c$ for $c\in\mathbb F_p$. It either has a root in the base field and splits completely, or is an <irreducible polynomial> of degree $p$.