Original scientific paper

https://doi.org/10.3336/gm.48.1.01

On geometric progressions on Pell equations and Lucas sequence

Attila Bérczes ; Institute of Mathematics, University of Debrecen, Number Theory Research Group, Hungarian Academy of Sciences and University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
Volker Ziegler ; Institute for Analysis and Computational Number Theory, Graz University of Technology, Steyrergasse 30/IV, A-8010 Graz, Austria

Abstract

We consider geometric progressions on the solution set of Pell equations and give upper bounds for such geometric progressions. Moreover, we show how to find for a given four term geometric progression a Pell equation such that this geometric progression is contained in the solution set. In the case of a given five term geometric progression we show that at most finitely many essentially distinct Pell equations exist, that admit the given five term geometric progression. In the last part of the paper we also establish similar results for Lucas sequences.

Keywords

Pell equations; geometric progressions; elliptic curves

Hrčak ID:

103265

URI

https://hrcak.srce.hr/103265

Publication date:

4.6.2013.

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