椭圆曲线整数点的递推序列及二次剩余法求解  

Search for the integral points on elliptic curve by recurrent sequences and quadratic residues

作　　者：董鑫 牟全武[1] DONG Xin;MU Quanwu(School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《西安工程大学学报》2020年第4期113-119,共7页Journal of Xi’an Polytechnic University

基　　金：陕西省自然科学基础研究计划项目(2019JM-337)。

摘　　要：研究了某种特殊类型的递推序列的同余性质。利用这些性质及二次剩余等初等数论方法与技巧,证明了Zagier提出的椭圆曲线y^2=x^3-30x+133的所有整数点是(x,y)=(-7,0),(-3,±14),(2,±9),(6,±13),(5143326,±11664498677)。Some congruence properties involving a special type of recurrent sequence are researched.Using these properties and some techniques about quadratic residues in elementary number theory,it is proved that all integral points on the elliptic curve y^2=x^3-30x+133 proposed by Zagier are(x,y)=(-7,0),(-3,±14),(2,±9),(6,±13),(5143326,±11664498677).

关 键 词：丢番图方程 椭圆曲线 递推序列 二次剩余 

分 类 号：O156.7[理学—数学]