ON THE DIOPHANTINE EQUATION x2-kxy+y2+2n=0

被引：3

作者：

Keskin, Refik ^{[1
]}

Karaatli, Olcay ^{[1
]}

Siar, Zafer ^{[1
]}

机构：

[1] Sakarya Univ, Fac Arts & Sci, TR-54187 Sakarya, Turkey

来源：

MISKOLC MATHEMATICAL NOTES | 2012年 / 13卷 / 02期

关键词：

Diophantine equations; Pell equations; generalized Fibonacci and Lucas numbers;

D O I：

10.18514/MMN.2012.433

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we determine when the equation in the title has an infinite number of positive integer solutions x and y when 0 <= n <= 10. Moreover, we give all the positive integer solutions of the same equation for 0 <= n <= 10.

引用

页码：375 / 388

页数：14

共 50 条

[21] ON THE DIOPHANTINE EQUATION 2(N)+PX(2)=Y(P)
LE, MH
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (02) : 321 - 326
[22] THE DIOPHANTINE EQUATION (bn)x + (2n)y = ((b+2)n)z
Tang, Min
Yang, Quan-Hui
COLLOQUIUM MATHEMATICUM, 2013, 132 (01) : 95 - 100
[23] On the diophantine equation (x(x-1)/2)(2)=y(y-1)/2
Luo, M
FIBONACCI QUARTERLY, 1996, 34 (03): : 277 - 279
[24] On the diophantine equation x 2+2 a • 3 b • 11 c = y n
Cangul, Ismail Naci
Demirci, Musa
Inam, Ilker
Luca, Florian
Soydan, Gokhan
MATHEMATICA SLOVACA, 2013, 63 (03) : 647 - 659
[25] A note on a theorem of Ljunggren and the Diophantine equations x2-kxy2+y4=1,4
Walsh, G
ARCHIV DER MATHEMATIK, 1999, 73 (02) : 119 - 125
[26] ON THE DIOPHANTINE EQUATION Z(2) = X(4)+DX(2)Y(2)+Y(4)
COHN, JHE
GLASGOW MATHEMATICAL JOURNAL, 1994, 36 : 283 - 285
[27] On the diophantine equation x2-Dy2 = n
Wei DaSheng
SCIENCE CHINA-MATHEMATICS, 2013, 56 (02) : 227 - 238
[28] A note on the diophantine equation ((x)(4))=((y)(2))
Pinter, AK
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1995, 47 (3-4): : 411 - 415
[29] On the diophantine equation x~2-Dy~2=n
WEI DaSheng
Science China(Mathematics), 2013, 56 (02) : 227 - 238
[30] On the Diophantine equation x(x+1) ••• (x + n)+1=y2
Abe, N
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2000, 76 (02) : 16 - 17

← 1 2 3 4 5 →