关于Pell方程ax^2-mqy^2=±1(m∈Z^+,3|a,q≡±1(mod6)是素数)

On Pell Equation ax^2-mqy^2=±1

Pell方程ax2-by2=±1(a,b∈Z+,ab不是完全平方数)可解性的判别是一个非常有意义的问题.本文运用Legendre符号和同余的性质给出了形如ax2-mqy2=±1(m∈Z+,3|a,q≡±1(mod 6)是素数,amq是非完全平方数)型Pell方程无正整数解的几个结论.这些结论对我们研究狭义Pell方程x2-Dy2=±1(D是非平方的正整数)起了重要作用.

The solubility of Pell equationax2-by2=±1(a,b∈Z+,abis a non-square positive integer)is a very meaningful question.It works out some methods to judge with the sets of Pell equation ax2-mqy2=±1(m∈Z+,3|a,q≡±1(mod12),pis a prime factor,amqis a non-square positive integer)witch they have not positive integer solution.These conclusions play an important role to research Pell equation x2-Dy2=±1(Dis a nonsquare positive integer).