Diophantine properties of linear recursive sequences II

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Abstract

Let Gn be a linear recursive sequence of integers and P(y) be a polynomial with integer coefficients. In this paper we are given a survey on results on the solutions of diophantine equation Gn = P(y). We prove especially that if Gn is of order three such that its characteristic polynomial is irreducible and has a dominating root then there are only finitely many perfect powers in Gn.

Original languageEnglish
Pages (from-to)81-96
Number of pages16
JournalActa Mathematica Academiae Paedagogicae Nyiregyhaziensis
Volume17
Issue number2
Publication statusPublished - Dec 1 2001

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Keywords

  • Linear forms in logarithms of algebraic numbers, subspace theorem
  • Linear recursive sequence, characteristic polynomial

ASJC Scopus subject areas

  • Mathematics(all)
  • Education

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