Abstract
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.
Citation
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. https://doi.org/10.11650/tjm/220303
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