Glasnik Matematicki, Vol. 43, No.2 (2008), 253-264.

FIBONACCI DIOPHANTINE TRIPLES

Florian Luca and László Szalay

Institute of Mathematics and Statistics, University of West Hungary, 9400, Sopron, Erzsébet utca 9, Hungary
e-mail: laszalay@ktk.nyme.hu

Abstract.   In this paper, we show that there are no three distinct positive integers a, b, c such that ab+1, ac+1, bc+1 are all three Fibonacci numbers.

2000 Mathematics Subject Classification.   11B37, 11B39, 11D61.

Key words and phrases.   Binary recurrences, Fibonacci and Lucas numbers, Diophantine triples.

DOI: 10.3336/gm.43.2.03

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