IMO Shortlist 1976 problem 8


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2. travnja 2012.
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Let P be a polynomial with real coefficients such that P(x) > 0 if x > 0. Prove that there exist polynomials Q and R with nonnegative coefficients such that \displaystyle P(x) = \frac{Q(x)}{R(x)} if x > 0.
Izvor: Međunarodna matematička olimpijada, shortlist 1976