Problem

Source: Iran MO 3rd round 2016 finals - Algebra P3

Tags: algebra, functional equation, function, Iran



Find all functions $f:\mathbb {R}^{+} \rightarrow \mathbb {R}^{+} $ such that for all positive real numbers $x,y:$ $$f(y)f(x+f(y))=f(x)f(xy)$$