两个Mordell方程的整数解OA
The Integer Solutions to Two Mordell Equations
Mordell方程y2=x3+k整数解是数论中历史悠久的问题.利用代数数论并结合整数的分解以及同余理论,证明了Mordell方程y2=x3-16 384有整数解(x,y)=(32,±128),(80,±704),以及Mordell方程y2=x3-81有整数解(x,y)=(13,±46).
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.
姜莲霞
喀什大学数学与统计学院,844000,新疆,喀什
数理科学
Mordell方程整数解代数数论
Mordell equationinteger solutionalgebraic number theory
《江西科学》 2026 (1)
93-96,4
新疆维吾尔自治区自然科学基金项目(2025D01A10).
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