2. The number of positive integer solutions to the equation $\frac{1}{x}+\frac{1}{y}=\frac{1}{2021}$ is $\qquad$ .
$x y=2021(x+y) \Rightarrow (x-2021)(y-2021)=2021^{2}=43^{2} \cdot 47^{2}$, so the number of positive integer solutions to this equation is 9.