Parametric solutions of Pell equations

2015/03/02 by Zapponi, Leonardo
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1503.00637

Abstract

This short paper is concerned with polynomial Pell equations P²-DQ²=1, with P,Q,D∈\Bbb C[X] and deg(D)=2. The main result shows that the polynomials P and Q are closely related to Chebyshev polynomials. We then investigate the existence of such polynomials in \Bbb Z[X] specializing to fixed solutions of ordinary Pell equations over the integers.

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