Czechoslovak Mathematical Journal, Vol. 71, No. 2, pp. 491-510, 2021
Chebyshev polynomials and Pell equations over finite fields
Boaz Cohen
Received October 10, 2019. Published online December 9, 2020.
Abstract: We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$ over finite fields of characteristic $p\neq2$. 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 $x^2-my^2=n$.
Affiliations: Boaz Cohen, Department of Computer Science, The Academic College of Tel-Aviv, Rabenu Yeruham St., P.O.Box 8401 Tel-Aviv Yaffo, 6818211, Israel, e-mail: arctanx@gmail.com