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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

Puni tekst: engleski, pdf (195 KB) str. 1-22 preuzimanja: 484* citiraj
APA 6th Edition
Bérczes, A. i Ziegler, V. (2013). On geometric progressions on Pell equations and Lucas sequence. Glasnik matematički, 48 (1), 1-22. https://doi.org/10.3336/gm.48.1.01
MLA 8th Edition
Bérczes, Attila i Volker Ziegler. "On geometric progressions on Pell equations and Lucas sequence." Glasnik matematički, vol. 48, br. 1, 2013, str. 1-22. https://doi.org/10.3336/gm.48.1.01. Citirano 27.10.2021.
Chicago 17th Edition
Bérczes, Attila i Volker Ziegler. "On geometric progressions on Pell equations and Lucas sequence." Glasnik matematički 48, br. 1 (2013): 1-22. https://doi.org/10.3336/gm.48.1.01
Harvard
Bérczes, A., i Ziegler, V. (2013). 'On geometric progressions on Pell equations and Lucas sequence', Glasnik matematički, 48(1), str. 1-22. https://doi.org/10.3336/gm.48.1.01
Vancouver
Bérczes A, Ziegler V. On geometric progressions on Pell equations and Lucas sequence. Glasnik matematički [Internet]. 2013 [pristupljeno 27.10.2021.];48(1):1-22. https://doi.org/10.3336/gm.48.1.01
IEEE
A. Bérczes i V. Ziegler, "On geometric progressions on Pell equations and Lucas sequence", Glasnik matematički, vol.48, br. 1, str. 1-22, 2013. [Online]. https://doi.org/10.3336/gm.48.1.01

Sažetak
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.

Ključne riječi
Pell equations; geometric progressions; elliptic curves

Hrčak ID: 103265

URI
https://hrcak.srce.hr/103265

Posjeta: 709 *