Question 105
Find all functions $f : (0; +\infty) \to \mathbf{R}$ such that the equality
$$
f(x)f(y) = f(xy) + 2005 \left( \frac{1}{x} + \frac{1}{y} + 2004 \right)
$$
holds for all positive real $x$ and $y$.
$$
f(x)f(y) = f(xy) + 2005 \left( \frac{1}{x} + \frac{1}{y} + 2004 \right)
$$
holds for all positive real $x$ and $y$.