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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the greatest prime factor of $(ab+1)(ac+1)$


Authors: P. Corvaja and U. Zannier
Journal: Proc. Amer. Math. Soc. 131 (2003), 1705-1709
MSC (2000): Primary 11J25
Published electronically: November 4, 2002
MathSciNet review: 1955256
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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 Györy, Sarkozy and Stewart, predicting the same conclusion for the product $(ab+1)(ac+1)(bc+1)$.


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Additional Information

P. Corvaja
Affiliation: Dipartimento di Matematica e Informatica, via delle Scienze, 206, 33100 Udine, Italy
Email: corvaja@dimi.uniud.it

U. Zannier
Affiliation: Istituto Universitario di Architettura di Venezia - DCA, S. Croce, 191, 30135 Venezia, Italy
Email: zannier@iuav.it

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06771-0
PII: S 0002-9939(02)06771-0
Received by editor(s): February 7, 2002
Published electronically: November 4, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society