IMO Shortlist 1969 problem 8


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2. travnja 2012.
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(BUL 2) Find all functions f defined for all x that satisfy the condition xf(y) + yf(x) = (x + y)f(x)f(y), for all x and y. Prove that exactly two of them are continuous.
Izvor: Međunarodna matematička olimpijada, shortlist 1969