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Keywords:
finite field; Chebyshev polynomial; Pell equation
Summary:
We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$ over finite fields of characteristic $p\neq 2$. 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 $x^2-my^2=n$.
References:
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[2] Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics 84. Springer, New York (1990). DOI 10.1007/978-1-4757-2103-4 | MR 1070716 | Zbl 0712.11001
[3] LeVeque, W. J.: Topics in Number Theory. Vol I. Dover Publications, Mineola (2002). MR 1942365 | Zbl 1009.11001
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