IMO Shortlist 2002 problem A2


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2. travnja 2012.
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Let a_1,a_2,\ldots be an infinite sequence of real numbers, for which there exists a real number c with 0\leq a_i\leq c for all i, such that

\left|\,a_i-a_j\,\right|\geq{1\over i+j}{\rm \forall}i,j \quad \textnormal{with} \quad i\ne j.

Prove that c\geq1.
Izvor: Međunarodna matematička olimpijada, shortlist 2002