2006 AIME A Problems/Problem 13

Revision as of 15:48, 25 September 2007 by 1=2 (talk | contribs) (Problem)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also