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

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

2006-07-18

arxiv.org/abs/math/0607413v1

Mathematics

Number Theory

6 pages

Scientific paper

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.

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