On the roots of certain Dickson polynomials

Aart Blokhuis, Xiwang Cao, Wun Seng Chou, Xiang Dong Hou

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

Let n be a positive integer, q=2n, and let Fq be the finite field with q elements. For each positive integer m, let Dm(X) be the Dickson polynomial of the first kind of degree m with parameter 1. Assume that m>1 is a divisor of q+1. We study the existence of α∈Fq such that Dm(α)=Dm−1)=0. We also explore the connections of this question to an open question by Wiedemann and a game called “Button Madness”.

Original languageEnglish
Pages (from-to)229-246
Number of pages18
JournalJournal of Number Theory
Volume188
DOIs
Publication statusPublished - 1 Jul 2018

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Keywords

  • Absolutely irreducible
  • Button madness
  • Dickson polynomials
  • Fermat number
  • Finite field
  • Reciprocal polynomial

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