关于Diophantine方程p^(2m)-Dx^2=1

On the Diophantine equation p^(2m)-Dx^2=1

设D是正整数,p是奇素数.运用初等方法讨论了方程p2 m-Dx2=1的正整数解(m,x)的个数,证明了该方程至多有1组正整数解(m,x).

Let D be a positive integer ,and let p be an odd prime .Using certain elementary methods ,the number of positive integer solutions （m ,x） of the equation p2m -Dx2 =1 is discussed .It proved that the equation has at most one positive integer solution （m ,x） .