On the Diophantine equation of the form

被引：0

作者：

Prugsapitak, Supawadee ^{[1
]}

Sangjan, Phitchayawee ^{[1
]}

机构：

[1] Prince Songkla Univ, Fac Sci, Div Computat Sci, Hat Yai, Thailand

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE | 2025年 / 20卷 / 01期

关键词：

Diophantine Equations; Calatan's Conjecture; Exponential Diophantine Equation;

D O I：

10.69793/ijmcs/01.2025/supawadee

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide the sufficient and necessary conditions for the existence of a solution to the Diophantine equation 4x ' x ' + (m2 m 2 - 1)x x = y2. 2 . Moreover, for an even positive integer m, we show that this equation can only be solved if and only if m is a prime power of 2. Furthermore, we provide all of its solutions.

引用

页码：187 / 190

页数：4