IMO Shortlist 2007 problem N4


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2. travnja 2012.
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For every integer k \geq 2, prove that 2^{3k} divides the number
\binom{2^{k + 1}}{2^{k}} - \binom{2^{k}}{2^{k - 1}}
but 2^{3k + 1} does not.

Author: unknown author, Poland
Izvor: Međunarodna matematička olimpijada, shortlist 2007