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Determine P(n+1)

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September 15, 2010
algebrapolynomialPolynomialsIMO Shortlist

Problem Statement

Let PP be a polynomial of degree nn satisfying P(k)=(n+1k)−1 for k=0,1,...,n.P(k) = \binom{n+1}{k}^{-1} \qquad \text{ for } k = 0, 1, . . ., n. Determine P(n+1).P(n + 1).
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