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Finiteness results for Diophantine triples with repdigit values

Volume 172 / 2016

Attila Bérczes, Florian Luca, István Pink, Volker Ziegler Acta Arithmetica 172 (2016), 133-148 MSC: Primary 11D61. DOI: 10.4064/aa8089-12-2015 Published online: 23 December 2015

Abstract

Let be an integer and \mathcal R_g\subset \mathbb{N} be the set of repdigits in base g. Let \mathcal D_g be the set of Diophantine triples with values in \mathcal R_g; that is, \mathcal D_g is the set of all triples (a,b,c)\in \mathbb{N}^3 with c \lt b \lt a such that ab+1, ac+1 and bc+1 lie in the set \mathcal R_g. We prove effective finiteness results for the set \mathcal D_g.

Authors

  • Attila BérczesInstitute of Mathematics
    University of Debrecen
    P.O. Box 12
    H-4010 Debrecen, Hungary
    e-mail
  • Florian LucaSchool of Mathematics
    University of the Witwatersrand
    Private Bag X3, Wits 2050
    Johannesburg, South Africa
    e-mail
  • István PinkInstitute of Mathematics
    University of Debrecen
    P.O. Box 12
    H-4010 Debrecen, Hungary
    and
    University of Salzburg
    Hellbrunnerstrasse 34/I
    A-5020 Salzburg, Austria
    e-mail
  • Volker ZieglerUniversity of Salzburg
    Hellbrunnerstrasse 34/I
    A-5020 Salzburg, Austria
    e-mail

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