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| − | == Problem ==
| + | #REDIRECT [[2006 AIME I Problems/Problem 13]] |
| − | For each [[even integer | even]] [[positive integer]] <math> x </math>, let <math> g(x) </math> denote the greatest power of 2 that [[divisor | divides]] <math> x. </math> For example, <math> g(20)=4 </math> and <math> g(16)=16. </math> For each positive integer <math> n, </math> let <math> S_n=\sum_{k=1}^{2^{n-1}}g(2k). </math> Find the greatest integer <math> n </math> less than 1000 such that <math> S_n </math> is a [[perfect square]].
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| − | == Solution ==
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| − | {{solution}}
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| − | == See also ==
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| − | *[[2006 AIME II Problems/Problem 14 | Next problem]]
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| − | *[[2006 AIME II Problems/Problem 12 | Previous problem]]
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| − | *[[2006 AIME II Problems]]
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| − | [[Category:Intermediate Number Theory Problems]]
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| − | [[Category:Intermediate Combinatorics Problems]]
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