Original scientific paper

https://doi.org/10.3336/gm.52.2.02

On Diophantine quadruples of Fibonacci numbers

Yasutsugu Fujita ; Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
Florian Luca orcid.org/0000-0003-1321-4422 ; School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa

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.

Keywords

Diophantine tuples; Fibonacci numbers; Subspace Theorem

Hrčak ID:

189329

URI

https://hrcak.srce.hr/189329

Publication date:

13.11.2017.

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