IMO Shortlist 2015 problem N1


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30. kolovoza 2018.
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Determine all positive integers M such that the sequence a_0, a_1, a_2, \cdots defined by a_0 = M + \frac{1}{2}   \qquad  \textrm{and} \qquad    a_{k+1} = a_k\lfloor a_k \rfloor   \quad \textrm{for} \, k = 0, 1, 2, \cdotscontains at least one integer term.

(Luxembourg)

Izvor: https://www.imo-official.org/problems/IMO2015SL.pdf