关于Pell方程qx^2-(qn±3)y^2=±1(q≡±1(mod6)是素数)

On Pell Equation qx^2-(qn±3)y^2=±1(q≡±1(mod6)Is a Prime Factor)

运用Legendre符号和同余的性质给出了形如qx2-(qn±3)y2=±1(q≡±1(mod6)是素数)型Pell方程无正整数解的四个结论。这些结论对研究狭义Pell方程x2-Dy2=±(1D是非平方的正整数)具有重要作用。

This paper works out four conclusions to judging the sets of Pell equation, q^x2-（qn ± 3）y^2= ± 1 （ q= ± 1 （mod6）Is a Prime Factor ）, which do not have positive integer solutions by applying related knowledge of legendre symbol and nature of congruence. These conclusions play an important role to research Pell equation x^2-Dy^2= ±1（D is a non-square positive integer）.