CAPS 2017 Problem 6

Find all functions ${f : (0, +\infty) \rightarrow R}$ satisfying $f(x) - f(x+ y) = f \left( \frac{x}{y}\right) f(x + y)$ for all $x, y > 0$ .

(Austria)

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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