@ARTICLE{Akkus, author = {Akkus, I. and Kilic, E. and Omur, N. and }, title = {Diophantine Equations Related with Linear Binary Recurrences}, volume = {17}, number = {1}, abstract ={In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh. }, URL = {http://ijmsi.ir/article-1-1319-en.html}, eprint = {http://ijmsi.ir/article-1-1319-en.pdf}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, doi = {10.52547/ijmsi.17.1.11}, year = {2022} }