IMO Shortlist 1991 problem 27


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2. travnja 2012.
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An infinite sequence \,x_{0},x_{1},x_{2},\ldots \, of real numbers is said to be bounded if there is a constant \,C\, such that \, \vert x_{i} \vert \leq C\, for every \,i\geq 0. Given any real number \,a > 1,\, construct a bounded infinite sequence x_{0},x_{1},x_{2},\ldots \, such that
\vert x_{i} - x_{j} \vert \vert i - j \vert^{a}\geq 1
for every pair of distinct nonnegative integers i, j.
Izvor: Međunarodna matematička olimpijada, shortlist 1991