# Article

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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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[3] LeVeque, W. J.: Topics in Number Theory. Vol I. Dover Publications, Mineola (2002). MR 1942365 | Zbl 1009.11001

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