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f(x) - f(x+ y) = f ( x / y) f(x + y) with x,y >0

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

September 28, 2017
functional equationpositiveFind all functionsalgebra

Problem Statement

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