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arXiv · 1503.00637

Parametric solutions of Pell equations

Leonardo Zapponi
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Abstract

This short paper is concerned with polynomial Pell equations \[P^2-DQ^2=1,\] with $P,Q,D\in\Bbb C[X]$ 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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Leonardo Zapponi. 2015-03-02. Parametric solutions of Pell equations. https://arxiv.org/abs/1503.00637

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