Volume 17, Issue 1 (4-2022)
IJMSI 2022, 17(1): 11-26 |
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Akkus I, Kilic E, Omur N. Diophantine Equations Related with Linear Binary Recurrences. IJMSI 2022; 17 (1) :11-26
URL: http://ijmsi.ir/article-1-1319-en.html
URL: http://ijmsi.ir/article-1-1319-en.html
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.
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.
Keywords: Linear recurrences, Generalized Fibonacci and Lucas sequences, Diophantine equations, Continued fractions.
Type of Study: Research paper |
Subject:
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