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

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