On the Diophantine equation x2 − kxy + y2 − 2n = 0

被引：0
|
作者：
Refik Keskin
Zafer Şiar
Olcay Karaatli
机构：
[1] Sakarya University,
[2] Bilecik Şeyh Edebali University,undefined
[3] Sakarya University,undefined
来源：
Czechoslovak Mathematical Journal | 2013年 / 63卷
关键词：
Diophantine equation; Pell equation; generalized Fibonacci number; generalized Lucas number; 11B37; 11B39; 11B50; 11B99;
D O I：
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中图分类号：
学科分类号：
摘要：
In this study, we determine when the Diophantine equation x2−kxy+y2−2n = 0 has an infinite number of positive integer solutions x and y for 0 ⩽ n ⩽ 10. Moreover, we give all positive integer solutions of the same equation for 0 ⩽ n ⩽ 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x2 − kxy + y2 − 2n = 0.
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页码：783 / 797
页数：14
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