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：
暂无
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.
引用
收藏
页码：783 / 797
页数：14
相关论文
共 50 条
  • [1] On the Diophantine equation x2 − kxy + y2 + lx = 0
    Yongzhong Hu
    Maohua Le
    Chinese Annals of Mathematics, Series B, 2013, 34 : 715 - 718
  • [2] On the Diophantine equation x2 - kxy plus y2-2n=0
    Keskin, Refik
    Siar, Zafer
    Karaatli, Olcay
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2013, 63 (03) : 783 - 797
  • [3] On the Diophantine equation x2 - kxy + y2 + lx=0, l ∈ {1,2,4}
    Yuan, Pingzhi
    Hu, Yongzhong
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (03) : 573 - 577
  • [4] ON THE DIOPHANTINE EQUATION x2-kxy+y2+2n=0
    Keskin, Refik
    Karaatli, Olcay
    Siar, Zafer
    MISKOLC MATHEMATICAL NOTES, 2012, 13 (02) : 375 - 388
  • [5] Solving the Diophantine equation y2 = x(x2 - n2)
    Draziotis, Konstantinos
    Poulakis, Dimitrios
    JOURNAL OF NUMBER THEORY, 2009, 129 (01) : 102 - 121
  • [6] On the Diophantine Equation Ax2 - KXY plus Y2 + Lx=0
    Urrutia, J. D.
    Aranas, J. M. E.
    Lara, J. A. C. L.
    Maceda, D. L. P.
    3RD INTERNATIONAL CONFERENCE ON SCIENCE & ENGINEERING IN MATHEMATICS, CHEMISTRY AND PHYSICS 2015 (SCITECH 2015), 2015, 622
  • [7] On the Diophantine equation x 2 - kxy plus y 2 + lx=0
    Hu, Yongzhong
    Le, Maohua
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2013, 34 (05) : 715 - 718
  • [8] On the Diophantine Equation x2-kxy+y2+lx=0
    Yongzhong HU
    Maohua LE
    Chinese Annals of Mathematics(Series B), 2013, 34 (05) : 715 - 718
  • [9] On ternary biquadratic Diophantine equation 11(x2 - y2)
    Vidhyalakshmi, S.
    Gopalan, M. A.
    Thangam, S. A.
    Ozer, O.
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2019, 25 (03) : 65 - 71
  • [10] On the Diophantine equations x2 - xy - y2 ± lx=0 and x2-3xy plus y2 ± lx=0
    Alibaud, Yaowaluk
    Prugsapitak, Supawadee
    Aukkhosuwan, Wuttichon
    SCIENCEASIA, 2020, 46 (04): : 490 - 493
12345