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Licensed Unlicensed Requires Authentication Published by De Gruyter September 27, 2020

Solutions of a generalized markoff equation in Fibonacci numbers

Hayder Raheem Hashim and Szabolcs Tengely
From the journal Mathematica Slovaca


In this paper, we find all the solutions (X, Y, Z) = (FI, FJ, FK), where FI, FJ, and FK represent nonzero Fibonacci numbers, satisfying a generalization of Markoff equation called the Jin-Schmidt equation: AX2 + BY2 + CZ2 = DXYZ + 1.

The authors would like to express their sincere gratitude to the referee for the careful reading of the manuscript and many useful comments, which improve the quality of the paper. This work was partially supported by the European Union and the European Social Fund through project EFOP-3.6.1-16-2016-00022 (Sz.T.). The research was supported in part by grants ANN130909, K115479 and K128088 (Sz.T.) of the Hungarian National Foundation for Scientific Research. The work of H. R. Hashim was supported by the Stipendium Hungaricum Scholarship.

  1. (Communicated by Milan Paštéka)


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Received: 2019-10-19
Accepted: 2020-02-05
Published Online: 2020-09-27
Published in Print: 2020-10-27

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