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Title: On the roots of certain Dickson polynomials
Authors: Blokhuis, Aart
Cao, Xiwang
Chou, Wun-Seng
Hou, Xiang-Dong
Tsai, Yun-Ching
Contributors: 應數系
Keywords: Absolutely irreducible;Button madness;Dickson polynomials;Fermat number;Finite field;Reciprocal polynomial
Date: 2018-07
Issue Date: 2018-07-24 17:31:04 (UTC+8)
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”.
Relation: Journal of Number Theory,Volume 188, Pages 229-246
Data Type: article
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Appears in Collections:[應用數學系] 期刊論文

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