# Problem #2113

 2113 Let $f$ be a function with the following properties: $(i) f(1) = 1$, and $(ii) f(2n) = n\times f(n)$, for any positive integer $n$. What is the value of $f(2^{100})$? $\text {(A)} 1 \qquad \text {(B)} 2^{99} \qquad \text {(C)} 2^{100} \qquad \text {(D)} 2^{4950} \qquad \text {(E)}2^{9999}$ This problem is copyrighted by the American Mathematics Competitions.
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