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1986 IMO Problems/Problem 5

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Find all (if any) functions $f$ taking the non-negative reals onto the non-negative reals, such that

(a) $f(xf(y))f(y) = f(x+y)$ for all non-negative $x$ , $y$ ;

(b) $f(2) = 0$ ;

(c) $f(x) \neq 0$ for every $0 \leq x < 2$ .

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