关于Pell方程qx^2-(qn±6)y^2=±1(q是素数)

On Pell equation qx^2-(qn±6)y^2=±1(q is a prime factor)

运用Legendre符号和同余的性质给出了形如qx2-(qn±6)y2=±1(q是素数)型Pell方程无正整数解的4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.

In this paper,by applying related knowledge of legendre sign and nature of congruence,it works out four conclusions to judge with the sets of Pell equation qx2-（qn±6）y2=±1（q is a prime factor） witch they have not positive integer solutions.These conclusions play an important role to research Pell equation x2-Dy2=±1（D is a non-square positive integer）.