A Generalized Fibonacci Sequence and the Diophantine Equations $x^2pm kxy-y^2pm x=0$

Author(s):

Mojtaba Bahramian , Hassan Daghigh

Message:
Abstract:
In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.
Keywords:

Diophantine equation , Generalized Fibonacci sequence , Pell equation

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:8 Issue: 2, Nov 2013
Pages:
111 to 121
https://www.magiran.com/p1186128