Question 30
How many pairs of positive integers $ (x, y) $ verify the equation
$$
x^{2}+y^{2}-2004 x-2004 y+2 x y-2005=0 ?
$$
Note: if $x \neq y$, the $(x, y)$ and $(y, x)$ pairs are to be considered different.
$$
x^{2}+y^{2}-2004 x-2004 y+2 x y-2005=0 ?
$$
Note: if $x \neq y$, the $(x, y)$ and $(y, x)$ pairs are to be considered different.