椭圆曲线y^2=nx(x^2-16)的整数点  

The Positive Integral Points on the Elliptic Curve y^2=nx(x^2-16)

作　　者：万飞[1] 李玉龙[1] WAN Fei;LI Yulong(College of Teachers Education,Honghe University,Mengzi 661199,China)

机构地区：[1]红河学院教师教育学院,云南蒙自661199

出　　处：《湖北民族学院学报（自然科学版）》2018年第1期49-51,共3页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：云南省教育厅科研基金项目(2014Y462);红河学院校级课题(XJ15Y22)

摘　　要：如果n为奇素数,利用初等方法得出了椭圆曲线y^2=nx(x^2-16),当n=5时,有整数点(x,y)=(0,0),(5,±15);当n=29时,有正整数点(x,y)=(0,0),(499,±41 801 760);n≠5,29时,仅有整数点(x,y)=(0,0).Let n be odd prime.Using elementary method,it was proved that if n=5,then the elliptic curve in title has integer points（0,0）,（5,±15）;if n=29,then the elliptic curve in title has integer points（0,0）,（499,±41 801 760）;if n≠5,29,then the elliptic curve in title only has integer point（0,0）.

关 键 词：椭圆曲线 整数点 奇素数 同余 

分 类 号：O156[理学—数学]