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2001 IMO Shortlist Problems/A4

Revision as of 18:14, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Find all functions <math>f: \mathbb{R} \rightarrow \mathbb{R}</math>, satisfying <center><math>f(xy)(f(x) - f(y)) = (x - y)f(x)f(y)</math></center> for all <math>x,y</math>. ...)

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Problem

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ , satisfying

$f(xy)(f(x) - f(y)) = (x - y)f(x)f(y)$

for all $x,y$ .

Solution

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