On the Diophantine equation (pq)x

被引：0

作者：

Orosram, Wachirarak ^{[1
]}

Tangjai, Wipawee ^{[2
]}

机构：

[1] Buriram Rajabhat Univ, Fac Sci, Dept Math, Buriram 31000, Thailand

[2] Mahasarakham Univ, Fac Sci, Dept Math, Maha Sarakham 44150, Thailand

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE | 2023年 / 18卷 / 02期

关键词：

Diophantine equation; non-negative integer solution; Catalan's conjectur;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the Diophantine equation ( pq)(x)+( pq)(2s) n(y) = z(2), where p and q are prime numbers such that pq = 3 (mod 20) and n = 5 (mod 20). We show that a non-negative integer solution of such equation exists only if pq + 1 is a square. The solution is also in the form ( x, y, z) = (1 + 2s, 0, ( pq)(s) root pq + 1).

引用

页码：143 / 147

页数：5

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