椭圆曲线y^2=(x+a)(x^2-ax+p)的大整数点  

A FAMILY OF ELLIPTIC CURVES WITH LARGE INTEGRAL POINTS

作　　者：冉银霞 RAN Yin-xia(Longnan Teachers College,College of Mathematics and Information Science,Chengxian,Gansu 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院,甘肃成县742500

出　　处：《井冈山大学学报（自然科学版）》2020年第6期6-9,共4页Journal of Jinggangshan University (Natural Science)

基　　金：甘肃省高等学校创新基金项目(2020-B367)。

摘　　要：确定椭圆曲线的有理点(尤其大整数点)是数论与算术代数几何中十分有趣的问题。尤其椭圆曲线在密码学等方面的应用中,针对不同的情况,需要构造不同的椭圆曲线。本文在这类椭圆曲线y^2=(x+a)(x^2-ax+p)中找到了一族有大整数点的椭圆曲线。同时得到了这族椭圆曲线有整数解的充要条件,且给出了8条椭圆曲线的大整数点。It is a very interesting problem to determine the rational points of elliptic curves(especially large integral points)in number theory and arithmetical algebraic geometry.Elliptic curve has been widely used in cryptography,etc.According to different situations,different elliptic curves are needed to construct.In this paper,a family of elliptic curves with large integer points is found,at the same time,the sufficient and necessary conditions for having integral solutions for the family of elliptic curves are found,and the large integral points of eight elliptic curves are given.

关 键 词：椭圆曲线 大整数点 同余 LEGENDRE符号 

分 类 号：O156.7[理学—数学]