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August, 2022 On the Exponential Diophantine Equation $F_{n+1}^x - F_{n-1}^x = F_m^y$
Carlos Alexis Gómez, Jhonny Carpediem Gómez, Florian Luca
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Taiwanese J. Math. 26(4): 685-712 (August, 2022). DOI: 10.11650/tjm/220303


In this paper, we find all the solutions of Diophantine equation written in our title, where $n$, $m$, $x$ and $y$ are positive integers and $F_k$ denotes the $k$th term of the Fibonacci sequence.

Funding Statement

C. A. Gómez was supported in part by Project 71331 (Universidad del Valle). J. C. Gómez was supported in part by Universidad Libre Seccional Pereira. F. Luca worked on this project while he was visiting IMB at the Université de Bordeaux in Fall 2021 as a CNRS visiting researcher. He was also supported in part by the ANR project JINVARIANT.


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Carlos Alexis Gómez. Jhonny Carpediem Gómez. Florian Luca. "On the Exponential Diophantine Equation $F_{n+1}^x - F_{n-1}^x = F_m^y$." Taiwanese J. Math. 26 (4) 685 - 712, August, 2022.


Received: 13 December 2021; Revised: 14 February 2022; Accepted: 9 March 2022; Published: August, 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.11650/tjm/220303

Primary: 11B39 , 11J86

Keywords: Diophantine exponential equation , Fibonacci numbers , linear form in logarithms , reduction method

Rights: Copyright © 2022 The Mathematical Society of the Republic of China


Vol.26 • No. 4 • August, 2022
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