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Intersections of recurrence sequences


Authors: Michael A. Bennett and Ákos Pintér
Journal: Proc. Amer. Math. Soc. 143 (2015), 2347-2353
MSC (2010): Primary 11J86, 11B39, 11D61
DOI: https://doi.org/10.1090/S0002-9939-2015-12499-9
Published electronically: January 21, 2015
MathSciNet review: 3326017
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Abstract: We derive sharp upper bounds for the size of the intersection of certain linear recurrence sequences. As a consequence of these, we partially resolve a conjecture of Yuan on simultaneous Pellian equations, under the condition that one of the parameters involved is suitably large.


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Additional Information

Michael A. Bennett
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1Z2
Email: bennett@math.ubc.ca

Ákos Pintér
Affiliation: Institute of Mathematics, MTA-DE Research Group “Equations, Functions and Curves”, Hungarian Academy of Sciences and University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
Email: apinter@science.unideb.hu

DOI: https://doi.org/10.1090/S0002-9939-2015-12499-9
Keywords: Recurrence sequences, simultaneous linear forms in logarithms
Received by editor(s): October 1, 2013
Received by editor(s) in revised form: January 19, 2014
Published electronically: January 21, 2015
Additional Notes: The first author was supported in part by a grant from NSERC
The second author was supported in part by the Hungarian Academy of Sciences, OTKA grants K100339, NK101680, NK104208 and by the European Union and the European Social Fund through project Supercomputer, the national virtual lab (grant no.: TÁMOP-4.2.2.C-11/1/KONV-2012-0010)
Communicated by: Matthew Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society