Glasnik Matematicki, Vol. 55, No. 1 (2020), 29-36.

MARKOFF-ROSENBERGER TRIPLES WITH FIBONACCI COMPONENTS

Szabolcs Tengely

Department of Mathematics, University of Debrecen, P.O.Box 12, 4010 Debrecen, Hungary
and
Department of Mathematics and Informatics, J. Selye University, Hradna ul. 21, 94501 Komarno, Slovakia
e-mail: tengely@science.unideb.hu

Abstract.   We characterize the solutions of the Markoff-Rosenberger equation

a x2 + b y2 + c z2 = d x y z

with a,b,c,d ∈ ℤ, gcd(a,b)=gcd(a,c)=gcd(b,c)=1 and a,b,c | d, for which (x,y,z)=(Fi,Fj,Fk), where Fn denotes the n-th Fibonacci number for any integer n≥ 0.

2010 Mathematics Subject Classification.   11D45, 11B39

Key words and phrases.   Fibonacci numbers, Markoff equation

Full text (PDF) (free access)

https://doi.org/10.3336/gm.55.1.03

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