1. On the roots of certain Dickson polynomials.
- Author
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Blokhuis, Aart, Cao, Xiwang, Chou, Wun-Seng, and Hou, Xiang-Dong
- Subjects
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DICKSON polynomials , *INTEGERS , *FINITE fields , *CONTINUOUS functions , *MATHEMATICAL analysis - Abstract
Let n be a positive integer, q = 2 n , and let F q be the finite field with q elements. For each positive integer m , let D m ( 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 ∈ F q ⁎ such that D m ( α ) = D m ( α − 1 ) = 0 . We also explore the connections of this question to an open question by Wiedemann and a game called “Button Madness”. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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