椭圆曲线y^(2)=7nx(x^(2)+32)的正整数点  

Positive Integer Points of Elliptic Curves y^(2)=7nx(x^(2)+32)

作　　者：余慧敏 张玲丽 过静[1] Yu Huiming;Zhang Lingli;Guo Jing(School of Big Date Science,Jiangxi Science&Technology Normal University,Nanchang 330038,Jiangxi,P.R.China)

机构地区：[1]江西科技师范大学大数据科学学院,江西南昌330038

出　　处：《江西科技师范大学学报》2023年第6期100-102,共3页Journal of Jiangxi Science & Technology Normal University

基　　金：江西省教育厅科学技术研究项目(GJJ211115)。

摘　　要：n为素数时关于椭圆曲线y^(2)=7nx(x^(2)+32)的整数点问题至今仍未解决。本文主要利用四次Diophantine方程的已知结果,运用Legendre符号的性质、奇偶数的性质、同余的性质、唯一分解定理等初等方法,证明了n≡5(mod 8)为奇素数时椭圆曲线y^(2)=7nx(x^(2)+32)至多有1个正整数点。When n is an odd prime,the integral points on elliptic curve y^(2)=7nx(x^(2)+32)still unresolved.In this paper,we use some known results of quartic Diophantine equation to obtain our results.by applying the elementary methods to the properties of Legendre symbol;the properties of even number and odd number;the properties of congruence and unique decomposition.It was proved that if n is an odd prime and n≡5(mod 8),then there are at most one positive integer point the elliptic curve in title.

关 键 词：椭圆曲线 正整数点 同余 LEGENDRE符号 

分 类 号：O156.1[理学—数学]