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Let S be the set of positive real numbers. Let \(f : S \to \mathbb{R}\) be a function such that \(f(x) f(y) = f(xy) + 2005 \left( \frac{1}{x} + \frac{1}{y} + 2004 \right)\) for all x,y, and 0.

Let n be the number of possible values of \(f(2)\), and let \(s \) be the sum of all possible values of f(2). Find \(n*s\).

 Oct 16, 2019
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The answer is 10.

 Oct 29, 2019

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