Irreducible factorization of translates of reversed Dickson polynomials over finite fields

Ron Evans; Mark Van Veen

Irreducible factorization of translates of reversed Dickson polynomials over finite fields

Number Theory 2018-02-07 v1

Authors: Ron Evans , Mark Van Veen

Abstract

Let $F$ be a field of $q$ elements, where $q$ is a power of an odd prime. Fix $n = (q+1)/2$ . For each $s \in F$ , we describe all the irreducible factors over $F$ of the polynomial $g_s(y): = y^n + (1-y)^n -s$ , and we give a necessary and sufficient condition on $s$ for $g_s(y)$ to be irreducible.

Keywords

finite fields dickson polynomials irreducible factorization reversed polynomials translates

Cite

@article{arxiv.1802.01739,
  title  = {Irreducible factorization of translates of reversed Dickson polynomials over finite fields},
  author = {Ron Evans and Mark Van Veen},
  journal= {arXiv preprint arXiv:1802.01739},
  year   = {2018}
}

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27 pages

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