Abstract
We shall describe how to construct a fundamental solution for the Pell equation x2 − my2 = 1 over finite fields of characteristic p ≠ 2. Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation x2 − my2 = n.
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References
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Acknowledgments
I wish to thank Prof. Marcel Herzog for his careful reading of the first draft of this paper. I also wish to thank the referee for his important remarks and suggestions.
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Cohen, B. Chebyshev Polynomials and Pell Equations over Finite Fields. Czech Math J 71, 491–510 (2021). https://doi.org/10.21136/CMJ.2020.0451-19
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DOI: https://doi.org/10.21136/CMJ.2020.0451-19