Problem

Source: Czech-Polish-Slovak Match 2017 day 2 P3

Tags: functional equation, positive, Find all functions, algebra



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)