方程p^(2x)-p^xD^y+D^(2y)=z^2的非负整数解

Nonnegative Integer Solutions of the Equation p^(2x)-p^xD^y+D^(2y)=z^2

设D是大于1的奇数,p是不能整除D的素数.文章给出了方程p2x-pxDy+D2y=z2有适合y>1的非负整数解(x,y,z)的充要条件.

Let D be an odd integer with D〉1, and let p be a prime with D≠0（mod）, this paper givs a necessary and sufficient condition for the equation p^2x-p^xD^y＋D^2y=z^2 to have the nonnegative integer solutions （ x, y, z ） with y 〉 1.