两条椭圆曲线的整点问题  

The Integral Points on the Two Elliptic Curves

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

机构地区：[1]陇南师范高等专科学校数信学院,成县742500

出　　处：《青岛大学学报（自然科学版）》2020年第3期3-7,共5页Journal of Qingdao University(Natural Science Edition)

基　　金：甘肃省高等学校创新基金(批准号2020-B367)资助。

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。利用同余、奇偶分析、二次同余式及二元二次方程解的结构及解序列的递归性质等初等方法得到了一类椭圆曲线中未解决的两个椭圆曲线没有正整数点的结论。It is a very interesting problem to determine the rational points of elliptic curves(especially large integer points)in number theory and arithmetical algebraic geometry.Elliptic curve has been widely used in cryptography,etc.According to different,situation,different,elliptic curves were needed to construct.By Using elementary methods including the properties of congruent,parity analysis,quadratic congruence,structure and sequence of solution for binary quadric equation,two unsolved elliptic curves in a class of the eliptic curves were solved,and the conclusion that these eliptic curves have no positiveinteger points wereproved.

关 键 词：椭圆曲线 整数点 二元二次方程 同余 

分 类 号：O156.7[理学—数学]