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Diophantine equations with Appell sequences

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Abstract

We consider the Diophantine equation \(P_n (x) = g(y)\) in \(x, y\) where \(P_n (x), g(x) \in \mathbb {Q}[x], \deg g(x) \ge 3\) and \(\left\{ P_n (x)\right\} _{n \ge 0}\) is an Appell sequence. Under some reasonable assumptions on \(P_n(x)\) we prove an ineffective finiteness result on the above equation.

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Acknowledgments

The first author was supported by the Hungarian Academy of Sciences and by the OTKA grant NK104208. The second author was partially supported by the European Union and the European Social Fund through project Supercomputer, the national virtual lab (grant no: T’AMOP-4.2.2.C-11/1/KONV-2012-0010).

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Authors and Affiliations

  1. Institute of Mathematics, MTA-DE Research Group “Equations Functions and Curves”, Hungarian Academy of Sciences and University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    András Bazsó

  2. Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    István Pink

Authors
  1. András Bazsó
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  2. István Pink
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Correspondence to András Bazsó.

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Bazsó, A., Pink, I. Diophantine equations with Appell sequences. Period Math Hung 69, 222–230 (2014). https://doi.org/10.1007/s10998-014-0047-y

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