Problem

Source: Czech and Slovak match

Tags: function, limit, algebra proposed, algebra



Find all functions $f: (1,\infty)\text{to R}$ satisfying $f(x)-f(y)=(y-x)f(xy)$ for all $x,y>1$.

HIDE: hint you may try to find $f(x^5)$ by two ways and then continue the solution. I have also solved by using this method.By finding $f(x^5)$ in two ways I found that $f(x)=xf(x^2)$ for all $x>1$.