6. The correct judgment about the positive integer solutions of the equation $1+2+\cdots+x=y^{2}$ is
A. None
B. 1
C. More than 1 but a finite number
D. Infinite
6. $\mathrm{D}$

Solution: It is easy to verify that $x=8, y=6$ is a positive integer solution to the equation, and if $x=x_{k}, y=y_{k}$ is a solution to the equation, then $x_{k+1}$ $=\left(2 x_{k}+1\right)^{2}-1, y_{k+1}=4 x_{k} y_{k}+2 y_{k}$ is also a solution to the equation.