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On Ternary Integral Recurrences

Volume 63 / 2015

A. Schinzel Bulletin Polish Acad. Sci. Math. 63 (2015), 19-23 MSC: Primary 11B37. DOI: 10.4064/ba63-1-3

Abstract

We prove that if $a,b,c,d,e,m$ are integers, $m>0$ and $(m,ac)=1$, then there exist infinitely many positive integers $n$ such that $m\mid (an+b)c^n-de^n$. Hence we derive a similar conclusion for ternary integral recurrences.

Authors

  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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