IMO Shortlist 1989 problem 16


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2. travnja 2012.
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The set \{a_0, a_1, \ldots, a_n\} of real numbers satisfies the following conditions:

(i) a_0 = a_n = 0,
(ii) for 1 \leq k \leq n - 1, a_k = c + \sum^{n-1}_{i=k} a_{i-k} \cdot \left(a_i + a_{i+1} \right)

Prove that c \leq \frac{1}{4n}.
Izvor: Međunarodna matematička olimpijada, shortlist 1989