IMO Shortlist 2003 problem N1


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2. travnja 2012.
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Let m be a fixed integer greater than 1. The sequence x_0, x_1, x_2, \ldots is defined as follows:

x_i=  2^i if 0 \leq i\leq m-1 and x_i = \sum_{j=1}^{m}x_{i-j}, if i\geq m.

Find the greatest k for which the sequence contains k consecutive terms divisible by m.
Izvor: Međunarodna matematička olimpijada, shortlist 2003



Komentari:

mislim, nije zapravo invalid, sam nema zadatka xd