%0 Journal Article %A Akkus, I. %A Kilic, E. %A Omur, N. %T Diophantine Equations Related with Linear Binary Recurrences %J Iranian Journal of Mathematical Sciences and Informatics %V 17 %N 1 %U http://ijmsi.ir/article-1-1319-en.html %R 10.52547/ijmsi.17.1.11 %D 2022 %K Linear recurrences, Generalized Fibonacci and Lucas sequences, Diophantine equations, Continued fractions., %X 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. %> http://ijmsi.ir/article-1-1319-en.pdf %P 11-26 %& 11 %! %9 Research paper %L A-10-3484-1 %+ Department of Mathematics, Faculty of Arts and Science, Kırıkkale University, TR-71450 Kırıkkale, Turkey %G eng %@ 1735-4463 %[ 2022