ON THE DIOPHANTINE EQUATION ax(3)

被引：1

作者：

Subburam, Sivanarayanapandian ^{[1
]}

Thangadurai, Ravindrananathan ^{[2
]}

机构：

[1] Inst Math Sci, CIT Campus, Chennai 600113, Tamil Nadu, India

[2] Harish Chandra Res Inst, Allahabad 211019, Uttar Pradesh, India

来源：

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2015年 / 53卷 / 01期

关键词：

Diophantine equations; positive solutions; upper bound for solutions; divisors in residue classes;

D O I：

10.7169/facm/2015.53.1.9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the diophantine equation ax(3) + by + c = xyz, where a, b and c are positive integers such that gcd (a, c) = 1 and c is square-free. Let (x, y, z) be a positive integral solution of the equation. In this paper, we shall give an upper bound for x, y and z in terms of the given inputs a, b and c. Also, we apply our results to investigate the divisors of the elements of the sequence {an(3) + c} in residue classes.

引用

页码：167 / 175

页数：9

共 50 条

[41] ON THE SOLUTIONS OF THE EXPONENTIAL DIOPHANTINE EQUATION ax + by = (m2+1)z
He, Bo
Togbe, Alain
Yang, Shichun
QUAESTIONES MATHEMATICAE, 2013, 36 (01) : 119 - 135
[42] The linear diophantine equation ax+by+cz=e IN Q(root 5)
Altindis, H
Atasoy, M
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1996, 27 (09): : 837 - 841
[43] Squares in Lehmer sequences and the Diophantine equation Ax4-By2=2
Yuan, Pingzhi
Li, Yuan
ACTA ARITHMETICA, 2009, 139 (03) : 275 - 302
[44] An upper bound for the number of solutions of the exponential diophantine equation ax+by=cz
Le, MH
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1999, 75 (06) : 90 - 91
[45] The matrix diophantine equations AX
Dzhaliuk, N. S.
Petrychkovych, V. M.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2011, 3 (02) : 49 - 56
[46] 关于Diophantine方程（ax3+1）/（ax+1）=f（y）
乐茂华
玉林师范学院学报, 2006, (03) : 1+12 - 1
[47] ON CONDITIONS OF DISCRETENESS AND THE DIOPHANTINE EQUATION AX2+BY2+CZ2=DXYZ
KERNISBERNER, G
ROSENBERGER, G
ARCHIV DER MATHEMATIK, 1980, 34 (06) : 481 - 493
[48] The Diophantine equation ax ± ay = zn when a is any non- negative integer
Laipaporn, Kittipong
Wananiyakul, Saeree
Khachorncharoenkul, Prathomjit
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2024, 32 (03): : 213 - 221
[49] THE NUMBER OF SOLUTIONS FOR THE DIOPHANTINE EQUATION AX2+BY2+CZ2=N
PEI, DY
KEXUE TONGBAO, 1983, 28 (09): : 1163 - 1167
[50] The linear diophantine-equation ax + by + cz = e in Q(u5)
Altindis, H.
Atasoy, M.
Indian Journal of Pure and Applied Mathematics, 27 (09):

← 1 2 3 4 5 →