IMO Shortlist 1991 problem 25


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2. travnja 2012.
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Let n \geq 2, n \in \mathbb{N} and let p, a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n \in \mathbb{R} satisfying \frac{1}{2} \leq p \leq 1, 0 \leq a_i, 0 \leq b_i \leq p, i = 1, \ldots, n, and \sum^n_{i=1} a_i = \sum^n_{i=1} b_i. Prove the inequality: \sum^n_{i=1} b_i \prod^n_{j = 1, j \neq i} a_j \leq \frac{p}{(n-1)^{n-1}}.
Izvor: Međunarodna matematička olimpijada, shortlist 1991