摘要
不定方程x3±8=Dy2(D不是完全平方数)可解性的判别是一个基本而重要的问题.此处运用递归序列和同余性质等初等方法证明了不定方程x3±8=109y2无适合gcd(x,y)=1的整数解;此结论对研究x3±8=Dy2的整数解问题起到了重要作用.
The solubility discrimination of the Diophantine equation x^3± 8 = 109y^2（ D is not a complete square number） is a very basic and meaningful question. In this paper,it is proved that there exists no integer solution for the Diophantine equation x^3± 8 = 109y^2with gcd（ x,y） = 1 by use of the elementary methods such as recursive sequence and congruence property and so on,which play an important role in studying integer solution for the Diophantine equation x^3± 8 = Dy^2.
出处
《重庆工商大学学报（自然科学版）》
2014年第5期26-28,共3页
Journal of Chongqing Technology and Business University:Natural Science Edition
关键词
不定方程
整数解
递归序列
Diophantine equation
integer solution
recurrent sequence
