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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the greatest prime factor of $(ab+1)(ac+1)$
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by P. Corvaja and U. Zannier
Proc. Amer. Math. Soc. 131 (2003), 1705-1709
DOI: https://doi.org/10.1090/S0002-9939-02-06771-0
Published electronically: November 4, 2002

Abstract:

We prove that for integers $a>b>c>0$, the greatest prime factor of $(ab+1)(ac+1)$ tends to infinity with $a$. In particular, this settles a conjecture raised by Gyรถry, Sarkozy and Stewart, predicting the same conclusion for the product $(ab+1)(ac+1)(bc+1)$.
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Bibliographic Information
  • P. Corvaja
  • Affiliation: Dipartimento di Matematica e Informatica, via delle Scienze, 206, 33100 Udine, Italy
  • MR Author ID: 327308
  • Email: corvaja@dimi.uniud.it
  • U. Zannier
  • Affiliation: Istituto Universitario di Architettura di Venezia - DCA, S. Croce, 191, 30135 Venezia, Italy
  • MR Author ID: 186540
  • Email: zannier@iuav.it
  • Received by editor(s): February 7, 2002
  • Published electronically: November 4, 2002
  • Communicated by: David E. Rohrlich
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1705-1709
  • MSC (2000): Primary 11J25
  • DOI: https://doi.org/10.1090/S0002-9939-02-06771-0
  • MathSciNet review: 1955256