IMO 1983 Problem 1

Day 1

Find all functions $f$ defined on the set of positive reals which take positive real values and satisfy: $f(xf(y))=yf(x)$ for all $x,y$ ; and $f(x)\to0$ as $x\to\infty$ .

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1983 official English paper, page 1.

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