IMO Shortlist 2011 problem N4


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23. lipnja 2013.
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For each positive integer k, let t(k) be the largest odd divisor of k. Determine all positive integers a for which there exists a positive integer n, such that all the differences

t(n+a)-t(n); t(n+a+1)-t(n+1), \ldots, t(n+2a-1)-t(n+a-1) are divisible by 4.

Proposed by Gerhard Wöginger, Austria
Izvor: Međunarodna matematička olimpijada, shortlist 2011