Glasnik Matematicki, Vol. 52, No. 2 (2017), 221-234.

ON DIOPHANTINE QUADRUPLES OF FIBONACCI NUMBERS

Yasutsugu Fujita and Florian Luca

Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
e-mail: fujita.yasutsugu@nihon-u.ac.jp

School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa,
Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany,
Department of Mathematics, Faculty of Sciences, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
e-mail: florian.luca@wits.ac.za

Abstract.   We show that there are only finitely many Diophantine quadruples, that is, sets of four positive integers {a1,a2,a3,a4} such that aiaj+1 is a square for all 1 ≤ i < j ≤ 4, consisting of Fibonacci numbers.

2010 Mathematics Subject Classification.   11D72, 11D61, 11B39, 11J87.

Key words and phrases.   Diophantine tuples, Fibonacci numbers, Subspace Theorem.

Full text (PDF) (free access)

DOI: 10.3336/gm.52.2.02

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