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.

中文翻译：

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有限域上的Chebyshev多项式和Pell方程

我们将描述如何在特征p ≠2的有限域上构造Pell方程x ² - my ² = 1的基本解。特别是，将使用Chebyshev多项式对这些基本解的结构进行完整描述。此外，我们将描述一般Pell方程x ² - my ² = n的解的结构。