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F from(1,infinity) to r

Source: Czech and Slovak match

February 9, 2006
functionlimitalgebra proposedalgebra

Problem Statement

Find all functions f:(1,∞)to Rf: (1,\infty)\text{to R} satisfying f(x)−f(y)=(y−x)f(xy)f(x)-f(y)=(y-x)f(xy) for all x,y>1x,y>1. [hide="hint"]you may try to find f(x5)f(x^5) by two ways and then continue the solution. I have also solved by using this method.By finding f(x5)f(x^5) in two ways I found that f(x)=xf(x2)f(x)=xf(x^2) for all x>1x>1.
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