IMO Shortlist 2006 problem A1


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2. travnja 2012.
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a_{0},\ a_{1},\ a_{2},\dots is a sequence of real numbers such that
a_{n + 1} = \left[a_{n}\right]\cdot \left\{a_{n}\right\}
prove that exist j such that for every i\geq j we have a_{i + 2} = a_{i}.
Izvor: Međunarodna matematička olimpijada, shortlist 2006