椭圆曲线y^(2)=(x-6)(x^(2)+6x+m)的整数点  

Integral Points on Elliptic Curve y^(2)=(x-6)(x^(2)+6x+m)

作　　者：王钊 杨海[1] 曹雅丽 WANG Zhao;YANG Hai;CAO Yali(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：《沈阳大学学报（自然科学版）》2022年第4期333-338,共6页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(11226038,11371012);陕西省自然科学基金资助项目(2021JM443)。

摘　　要：设m=30s^(2)-7,其中s是使6s^(2)+13及15s^(2)-8为奇素数的正奇数,结合初等数论方法及二元四次丢番图方程的结论,证明了椭圆曲线y^(2)=(x-6)(x^(2)+6x+m)除整数点(x,y)=(6,0)外无其他非平凡整数点。Let m=30s^(2)-7,where s is a positive odd number such that 6s^(2)+13 and 15s^(2)-8 are odd primes.Combined with the method of elementary number theory and the conclusion of the binary quadratic Diophantine equation,it is proved that the elliptic curve y^(2)=(x-6)(x^(2)+6x+m)has no other non-trivial integer points except the integer point(x,y)=(6,0).

关 键 词：椭圆曲线 整数点 同余 二次剩余 丢番图方程 

分 类 号：O156.1[理学—数学]