Diophantine triples in linear recurrences of Pisot type View Full Text


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Article Info

DATE

2018-06-25

AUTHORS

Clemens Fuchs, Christoph Hutle, Florian Luca

ABSTRACT

The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence or finiteness of Diophantine triples in such sequences. Whilst the case of binary recurrence sequences is almost completely solved, not much was known about recurrence sequences of larger order, except for very specialised generalisations of the Fibonacci sequence. Now, we will prove that any linear recurrence sequence with the Pisot property contains only finitely many Diophantine triples, whenever the order is large and a few more not very restrictive conditions are met. More... »

PAGES

29

References to SciGraph publications

  • 2016-08-04. Diophantine Triples and k-Generalized Fibonacci Sequences in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • 2002-08. Finiteness of integral values for the ratio of two linear recurrences in INVENTIONES MATHEMATICAE
  • 2015-01-06. Balancing Diophantine triples with distance 1 in PERIODICA MATHEMATICA HUNGARICA
  • 1992. Pisot and Salem Numbers in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40993-018-0121-2

    DOI

    http://dx.doi.org/10.1007/s40993-018-0121-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1105106715

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30393755


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