江西科学2026，Vol.44Issue(1)：93-96,4.DOI:10.13990/j.issn1001-3679.2026.01.013
两个Mordell方程的整数解
The Integer Solutions to Two Mordell Equations
摘要
Abstract
The problem of integer solutions for the Mordell equation y2=x3+k is a long standing problem in number theory.By using algebraic number theory and combining inte-ger decomposition and congruence theory,the Mordell equation y2=x3-16 384 has integer solutions(x,y)=(32,±128),(80,±704),and the Mordell equation y2=x3-81 has inte-ger solutions(x,y)=(13,±46)were proved.关键词
Mordell方程/整数解/代数数论Key words
Mordell equation/integer solution/algebraic number theory分类
数理科学引用本文复制引用
姜莲霞..两个Mordell方程的整数解[J].江西科学,2026,44(1):93-96,4.基金项目
新疆维吾尔自治区自然科学基金项目(2025D01A10). （2025D01A10）
