On the Exponential Diophantine Equation F-n+1(x) - F-n-1(x) = F-m(y)

Carlos Alexis Gomez; Jhonny Carpediem Gomez; Florian Luca

doi:10.11650/tjm/220303

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On the Exponential Diophantine Equation F-n+1(x) - F-n-1(x) = F-m(y)

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On the Exponential Diophantine Equation F-n+1(x) - F-n-1(x) = F-m(y)

Carlos Alexis Gomez, Jhonny Carpediem Gomez and Florian Luca

Taiwanese journal of mathematics, Vol.26(4), pp.685-712

01/08/2022

DOI: https://doi.org/10.11650/tjm/220303

Abstract

Mathematics

Physical Sciences

Science & Technology

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 kth term of the Fibonacci sequence.

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Title: On the Exponential Diophantine Equation F-n+1(x) - F-n-1(x) = F-m(y)
Creators - without role: Carlos Alexis Gomez - University of Valle
Jhonny Carpediem Gomez - Univ Libre Secc Pereira, Fac Ciencias Econ Adm & Contables, Ave Amer Carrera 28 96-102, Pereira, Colombia
Florian Luca - King Abdulaziz University
Publication Details: Taiwanese journal of mathematics, Vol.26(4), pp.685-712
Publisher: Mathematical Soc Rep China
Number of pages: 28
Grant note: ANR project JINVARIANT; French National Research Agency (ANR) 71331 / Universidad del Valle Universidad Libre Seccional Pereira
Identifiers: 9937901908331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article