Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1401
1
1
gregorian
2022
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1
17
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online
1
fulltext
en
Diophantine Equations Related with Linear Binary Recurrences
عمومى
General
پژوهشي
Research paper
In this paper we find all solutions of four kinds of the Diophantine equations<br>
begin{equation*}<br>
~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0,<br>
end{equation*}%<br>
for an odd number $t$, and,<br>
begin{equation*}<br>
~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0,<br>
end{equation*}%<br>
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.
Linear recurrences, Generalized Fibonacci and Lucas sequences, Diophantine equations, Continued fractions.
11
26
http://ijmsi.ir/browse.php?a_code=A-10-3484-1&slc_lang=en&sid=1
I.
Akkus
iakkus.tr@gmail.com
10031947532846009211
10031947532846009211
Yes
Department of Mathematics, Faculty of Arts and Science, Kırıkkale University, TR-71450 Kırıkkale, Turkey
E.
Kilic
ekilic@etu.edu.tr
10031947532846009212
10031947532846009212
No
Department of Mathematics, TOBB University of Economics and Technology, TR-06560 Ankara, Turkey
N.
Omur
neseomur@kocaeli.edu.tr
10031947532846009213
10031947532846009213
No
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, TR-41380 Kocaeli, Turkey