La factorisation de $x^{p^l}-x\in \mathbb{F}\_p[x]$ selon la trace

Abstract

We present a few factorizations of polynomials over finite fields. These factorizations are related to traces, compositions of polynomials and binomial coefficients. As a corollary we obtain a description of all irreducible polynomials $Q\in \mathbb{F}\_2[x]$ such that $Q(1+x+x^2)$ (or $Q(x+x^2)$) remain irreducible.

6 pages