摘要
目的椭圆曲线的整数点是数论中的一个重要问题。关于椭圆曲线y2=nx(xI2-2)的整数点问题至今仍未解决。方法利用同余、Legendre符号的性质等初等方法。结果证明n≡3(mod8)为奇素数时椭圆曲线y2=nx(x2-2)无正整数点;n≡5(mod8)为奇素数时椭圆曲线y2=nx(x2-2)至多有2个正整数点。结论此结果推进了该类椭圆曲线的研究。
Objective The integral points on elliptic curve is a very important problem of Number The-ory.The integral points on elliptic curve y2 =nx(x2-2)still remain unresolved.Methods Properties of the solutions to congruence and Legendre symbol.Results It is proved that if n is an odd prime and n≡3 (mod8),then the elliptic curve in title has no positive integeral points;if is an odd prime and n ≡5(mod8),then the elliptic curve in title has at most two positive integeral points.Conclusion These re-sults promote the study on the kind of elliptic curve.
出处
《河北北方学院学报（自然科学版）》
2016年第3期10-11,20,共3页
Journal of Hebei North University:Natural Science Edition
基金
云南省教育厅科学研究项目(2014Y462)
关键词
椭圆曲线
正整数点
奇素数
elliptic curve
integeral point
odd prime
