Difference between revisions of "2006 AIME I Problems/Problem 13"

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== See also ==
 
== See also ==
* [[2006 AIME I Problems/Problem 12 | Previous problem]]
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{{AIME box|year=2006|n=I|num-b=12|num-a=14}}
* [[2006 AIME I Problems/Problem 14 | Next problem]]
 
* [[2006 AIME I Problems]]
 
  
 
[[Category:Intermediate Number Theory Problems]]
 
[[Category:Intermediate Number Theory Problems]]

Revision as of 22:17, 11 March 2007

Problem

For each even positive integer $x$, let $g(x)$ denote the greatest power of 2 that divides $x.$ For example, $g(20)=4$ and $g(16)=16.$ For each positive integer $n,$ let $S_n=\sum_{k=1}^{2^{n-1}}g(2k).$ Find the greatest integer $n$ less than 1000 such that $S_n$ is a perfect square.


Solution

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See also

2006 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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All AIME Problems and Solutions