Article ID Journal Published Year Pages File Type
8896924 Journal of Number Theory 2018 18 Pages PDF
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”.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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