关于方程组x^2-Dy^2=1-D和x^2=2z^2-1的正整数解

On the Positive Integer Solutions of the System of Equations x^2-Dy^2=1-D and x=2z^2-1

设D是可使D-1是奇素数方幂的正整数,给出了确定方程组x2-Dy2=1-D和x2=2z2-1的全部正整数解(x,y,z)的一般方法.

Let D be a positive integer such that D-1 is an odd prime power.In this paper we give a general method to find all positive integer solutions(x,y,z) of the system of equations x^2-Dy^2=1-D and x=2z^2-1.