联立Pell方程组x^2-Dy^2=-1和z^2-(D+4)y^2=-1

The Simultaneous Pell Equations x^2-Dy^2=-1 and z^2-(D+4)y^2=-1

设D是正奇数.该文证明了:如果D≡1(mod8),则方程组x2-Dy2=-1和z2-(D+4)y2=-1没有整数解.

Let D be a positive odd integer. In this paper we prove that if D=1（mod8）, then the equations x^2 - Dy^2 = - 1 and z^2 - （ D ＋ 4） y^2 = - 1 have no integer solution （ x, y, z）.