%0 Journal Article
%T Explicit factorization of $x^n-1\in \mathbb F_q[x]$
%A F. E. Brochero Mart¨ªnez
%A C. R. Giraldo Vergara
%A L. Batista de Oliveira
%J Mathematics
%D 2014
%I arXiv
%X Let $\mathbb F_q$ be a finite field and $n$ a positive integer. In this article, we prove that, under some conditions on $q$ and $n$, the polynomial $x^n-1$ can be split into irreducible binomials $x^t-a$ and an explicit factorization into irreducible factors is given. Finally, weakening one of our hypothesis, we also obtain factors of the form $x^{2t}-ax^t+b$ and explicit splitting of $x^n-1$ into irreducible factors is given.
%U http://arxiv.org/abs/1404.6281v2