دوره 17، شماره 1 - ( 1-1401 )
جلد 17 شماره 1 صفحات 26-11 |
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چکیده:
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.
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