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Chebyshev polynomials and Pell equations over finite fields. (English) Zbl 07361081

In this paper, the author describes the construction of the fundamental solution for the Pell equation over finite fields of characteristic different from 2. The description is given in terms of Chebyshev polynomials.

MSC:

12E20 Finite fields (field-theoretic aspects)
11D09 Quadratic and bilinear Diophantine equations
12E10 Special polynomials in general fields
11T99 Finite fields and commutative rings (number-theoretic aspects)
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References:

[1] Benjamin, A. T.; Walton, D., Counting on Chebyshev polynomials, Math. Mag. 82 (2009), 117-126 · Zbl 1223.33013
[2] Ireland, K.; Rosen, M., A Classical Introduction to Modern Number Theory, Graduate Texts in Mathematics 84. Springer, New York (1990) · Zbl 0712.11001
[3] LeVeque, W. J., Topics in Number Theory. Vol I, Dover Publications, Mineola (2002) · Zbl 1009.11001
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