Glasnik matematički, Vol. 55 No. 1, 2020.
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
Publication date:
12.6.2020.
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