Original scientific paper

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

Markoff-Rosenberger triples with Fibonacci components

Szabolcs Tengelys ; 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

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.

Keywords

Fibonacci numbers; Markoff equation

Hrčak ID:

239040

URI

https://hrcak.srce.hr/239040

Publication date:

12.6.2020.

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