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 IMO Shortlist 2011, Number Theory 4
11-20-2012, 11:54 AM
Post: #1
 elim Moderator Posts: 581 Joined: Feb 2010 Reputation: 0
IMO Shortlist 2011, Number Theory 4

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 $\quad$ src
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 Messages In This Thread IMO Shortlist 2011, Number Theory 4 - elim - 11-20-2012 11:54 AM Solution by nunoarala: IMO Shortlist 2011, Number Theory 4 - elim - 11-20-2012, 12:20 PM

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