On the Diophantine Equation x(2)

被引：0

作者：

Yow, K. S. ^{[1
]}

Sapar, S. H. ^{[1
]}

Atan, K. A. ^{[1
]}

机构：

[1] Univ Putra Malaysia, Inst Math Res, Serdang 43400, Selangor, Malaysia

来源：

PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY | 2013年 / 21卷 / 02期

关键词：

Diophantine equation; generator; geometric progression;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper investigates and determines the solutions for the Diophantine equation x(2) + 4 center dot 7(b )= y(2r), where x,y, b are all positive intergers and r > 1. By substituting the values of r and b respectively, generators of x and y can be determined and classified into different categories. Then, by using geometric progression method, a general formula for each category can be obtained. The necessary conditions to obtain the integral solutions of x and y are also investigated.

引用

页码：443 / 457

页数：15

共 12 条

[1]

Abu Muriefah FS, 1998, B AUST MATH SOC, V57, P189

[2]

Arif S.A., 1998, INT J MATH MATH SCI, V21, P610

[3] THE DIOPHANTINE EQUATION X(2)+C=Y(N) [J].

COHN, JHE .

ACTA ARITHMETICA, 1993, 65 (04) :367-381

[4]

KO C, 1965, SCI SINICA, V14, P457

[5]

Le MH, 1997, CHINESE SCI BULL, V42, P1515

[6]

Lebesgue V. A., 1850, NOUVELLA ANN MATHEME, V78, P26

[7]

Ljunggren W., 1943, ARK MAT ASTR FYS A, V29A

[8] On a diophantine equation [J].

Luca, F .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2000, 61 (02) :241-246

[9]

Luca F, 2002, INT J MATH MATH SCI, V29, P239

[10] ON THE DIOPHANTINE EQUATION x2+2a . 5b = yn [J].

Luca, Florian ;

Togbe, Alain .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2008, 4 (06) :973-979

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