On the diophantine equation ax3+by+c=xyz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ax^{3} + by + c = xyz$$\end{document}

被引：0

作者：

S. Subburam

A. Togbé

机构：

[1] C.I.T Campus,The Institute of Mathematical Sciences

[2] Purdue University North Central,Mathematics Department

来源：

Afrika Matematika | 2017年 / 28卷 / 1-2期

关键词：

Diophantine equations; Divisors; Residue classes; Primary 11D25; 11D45;

D O I：

10.1007/s13370-016-0423-2

中图分类号：

学科分类号：

摘要：

In this paper, we study the diophantine equation ax3+by+c=xyz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ax^{3} + by + c = xyz$$\end{document} and we produce an upper bound for the number of positive integral solutions (x, y, z) of the equation. Through this, we study a conjecture of A. Togbé concerning the number of positive integral solutions (x, y, z) of the equation when a=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a= 1$$\end{document} and c=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c = 4$$\end{document}.

引用

页码：9 / 21

页数：12

共 9 条

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[8]

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[9]

Utz WR(undefined)undefined undefined undefined undefined-undefined

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