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    Please use this identifier to cite or link to this item: http://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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