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On the roots of certain Dickson polynomials

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 2018 Taiwan, Netherlands English Publisher:Elsevier BVJournal:Journal of Number Theory, volume 188, pages 229-246 (issn: 0022-314X,

Authors: Blokhuis, Aart; Cao, Xiwang; Chou, Wun-Seng; Hou, Xiang-Dong; Tsai, Yun-Ching;

doi: 10.1016/j.jnt.2018.01.003

On the roots of certain Dickson polynomials

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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(α−1)=0. We also explore the connections of this question to an open question by Wiedemann and a game called “Button Madness”.

Countries

Taiwan, Netherlands

Related Organizations

Florida Southern College
United States
Eindhoven University of Technology
Netherlands
Chinese Academy of Sciences
China (People's Republic of)
National Chengchi University
Taiwan
Technical University Eindhoven
Netherlands

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Keywords

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

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