TY - JOUR
T1 - Diophantine Equations Related with Linear Binary Recurrences
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 1
UR - http://ijmsi.ir/article-1-1319-en.html
Y1 - 2022
SP - 11
EP - 26
KW - Linear recurrences
KW - Generalized Fibonacci and Lucas sequences
KW - Diophantine equations
KW - Continued fractions.
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.
M3 10.52547/ijmsi.17.1.11
ER -