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Local-global principles for recurrence sequences

Volume 67 / 2019

A. Schinzel, M. Skałba Bulletin Polish Acad. Sci. Math. 67 (2019), 37-40 MSC: Primary 11B39. DOI: 10.4064/ba8179-1-2019 Published online: 14 February 2019

Abstract

A proof is given that if a non-degenerate recurrence sequence of the second order over the rationals with separable companion equation contains multiples of infinitely many terms of the Lucas sequence governed by the same recurrence, then it contains zero for an index of a suitable sign.

Authors

  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail
  • M. SkałbaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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