IMO Shortlist 1997 problem 10


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2. travnja 2012.
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Find all positive integers k for which the following statement is true: If F(x) is a polynomial with integer coefficients satisfying the condition 0 \leq F(c) \leq k for each c\in \{0,1,\ldots,k + 1\}, then F(0) = F(1) = \ldots = F(k + 1).
Izvor: Međunarodna matematička olimpijada, shortlist 1997