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Problem: 2004 AMC 10 #24

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February 1, 2007
easiest p24

Problem Statement

Let a1,a2,⋯a_1, a_2, \cdots, be a sequence with the following properties.
I. a1=1a_1 = 1, and II. a2n=n⋅ana_{2n}=n\cdot a_n for any positive integer nn.
What is the value of a2100a_{2^{100}}?
<spanclass=′latex−bold′>(A)</span>  1<spanclass=′latex−bold′>(B)</span>  299<spanclass=′latex−bold′>(C)</span>  2100<spanclass=′latex−bold′>(D)</span>  24950<spanclass=′latex−bold′>(E)</span>  29999 <span class='latex-bold'>(A)</span>\; 1\qquad <span class='latex-bold'>(B)</span>\; 2^{99}\qquad <span class='latex-bold'>(C)</span>\; 2^{100}\qquad <span class='latex-bold'>(D)</span>\; 2^{4950}\qquad <span class='latex-bold'>(E)</span>\; 2^{9999}
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