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

Roland Bacher (1)

1 IF - Institut Fourier

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.

Mots clés: trace; factorization; finite field; binomial coefficient

Domaines: Théorie des nombres [math.NT]

Roland Bacher. La factorisation de $x^{p^l}-x\in{\mathbb F}_p[x]$ selon la trace. 2006. ⟨hal-00086129⟩