关于Pell方程Ax^2-By^2=±1(A,B∈Z^+)

On Pell Equation Ax^2-By^2=±1(A,B∈Z^+)

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.运用Legendre符号和同余性质等初等方法给出了形如Ax2-By2=±1(A,B∈Z+,AB不是完全平方数)型Pell方程无正整数解的6个结论.这些结论对研究狭义Pell方程x2-Dy2=±1(D不是完全平方数)起了重要作用.

The solubility of Pell equation Ax^2-By^2=±1（A,B∈Z^＋,AB is a non-square positive integer）is a very meaningful question. In this paper,it works out six conclusions that Pell equation such as Ax^2-By^2=±1（A,B∈Z^＋ ,AB is a non-square positive integer） has no positive integer solation by using the elementary method of Legendre symbol and property of congruence, which play an important role in studying special Pell equation Ax^2 - By^2 = ± 1 （ A,B ∈ Z^＋ ,AB is a non-square positive integer）.