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

Revision as of 20:26, 4 July 2006

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.

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

Revision as of 20:26, 4 July 2006

Problem

Solution

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Revision as of 11:15, 30 June 2006 (view source) MCrawford (talk \| contribs) m ← Older edit	Revision as of 20:26, 4 July 2006 (view source) Joml88 (talk \| contribs) m (2006 AIME I Problem 13 moved to 2006 AIME I Problems/Problem 13) Newer edit →
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