Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametric solutions of Pell equations   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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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex