TY - JOUR JF - IJMSI JO - IJMSI VL - 17 IS - 1 PY - 2022 Y1 - 2022/4/01 TI - Diophantine Equations Related with Linear Binary Recurrences TT - N2 - 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. SP - 11 EP - 26 AU - Akkus, I. AU - Kilic, E. AU - Omur, N. AD - Department of Mathematics, Faculty of Arts and Science, Kırıkkale University, TR-71450 Kırıkkale, Turkey KW - Linear recurrences KW - Generalized Fibonacci and Lucas sequences KW - Diophantine equations KW - Continued fractions. UR - http://ijmsi.ir/article-1-1319-en.html DO - 10.52547/ijmsi.17.1.11 ER -