On the Diophantine Equation Gn(x) = Gm(P(x)) View Full Text


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Article Info

DATE

2002-11

AUTHORS

Clemens Fuchs, Attila Pethö, Robert F. Tichy

ABSTRACT

. Let K be a field of characteristic 0 and let p, q, G0, G1, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (Gn(x))n=0∞ be defined by the second order linear recurring sequence\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}In this paper we give conditions under which the diophantine equation Gn(x) = Gm(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}In the last part we specialize our results to certain families of orthogonal polynomials. More... »

PAGES

173-196

References to SciGraph publications

  • 1999-09. The zero multiplicity of linear recurrence sequences in ACTA MATHEMATICA
  • 1997-06. The multiplicity of binary recurrences in INVENTIONES MATHEMATICAE
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00605-002-0497-9

    DOI

    http://dx.doi.org/10.1007/s00605-002-0497-9

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