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政大典藏 > College of Science > Department of Mathematical Sciences > Periodical Articles > Item 140.119/118885

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/118885

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
DOI link:	https://doi.org/10.1016/j.jnt.2018.01.003
DOI:	10.1016/j.jnt.2018.01.003
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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