IMO Shortlist 1990 problem 25


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2. travnja 2012.
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Let {\mathbb Q}^ + be the set of positive rational numbers. Construct a function f : {\mathbb Q}^ + \rightarrow {\mathbb Q}^ + such that
f(xf(y)) = \frac {f(x)}{y}
for all x, y in {\mathbb Q}^ +.
Izvor: Međunarodna matematička olimpijada, shortlist 1990