摘要
Pell方程ax2-by2=±1(a,b∈Z+,a,b不是完全平方数)可解性的判别是一个非常有意义的问题.运用Legendre符号和同余的性质给出了形如ax2-mqy2=±1(m∈Z+,2 a,q≡±1(mod4)是素数,a,m,q是非完全平方数)型Pell方程无正整数解的几个结论.这些结论对研究狭义Pell方程x2-Dy2=±1(D是非平方的正整数)起了重要作用.
The discrimination of solubility of Pell equation ax^2-by^2=±1(a,b∈Z^+,ab is not a perfect square positive integer) is a very meaningful question.In this paper,by applying related knowledge of Legendre sign and nature of congruence,it works out several conclusions that Pell equation such as ax^2-mqy^2=±1(m∈Z^+,2a,q≡±1(mod 4),p is a prime factor,a,m,q is not perfect square number) has not positive integer solution.These conclusions play an important role in studying restricted Pell equation x2-Dy2=±1(D is a non-square positive integer).
出处
《重庆工商大学学报(自然科学版)》
2012年第10期11-15,共5页
Journal of Chongqing Technology and Business University:Natural Science Edition
基金
云南省教育厅科研基金(2011C121)