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Diophantine equations with products of consecutive members of binary recurrences |
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| Authors: | Attila Bérczes Yuri F. Bilu Florian Luca |
| Affiliation: | 1.Institute of Mathematics,University of Debrecen,Debrecen,Hungary;2.Institut de Mathématiques de Bordeaux,Université de Bordeaux and CNRS,Talence,France;3.School of Mathematics,University of the Witwatersrand,Wits,South Africa;4.Max Planck Institute for Mathematics,Bonn,Germany;5.Department of Mathematics, Faculty of Sciences,University of Ostrava,Ostrava 1,Czech Republic |
| Abstract: | We prove a finiteness result for the number of solutions of a Diophantine equation of the form (u_n u_{n+1}cdots u_{n+k}pm 1 =pm u_m^2), where ({ u_n}_{nge 1}) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units. |
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