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
收藏
页码：143 / 147
页数：5
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