Glasnik matematički, Vol. 52 No. 2, 2017.
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
Publication date:
13.11.2017.
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