Czechoslovak Mathematical Journal, first online, pp. 1-20
Chebyshev polynomials and Pell equations over finite fields
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 $x^2-my^2=n$.