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2020 AMC 10A Problems/Problem 21

Revision as of 20:57, 31 January 2020 by Luckylw (talk | contribs) (Created page with "There exists a unique strictly increasing sequence of nonnegative integers <math>a_1 < a_2 < … < a_k</math> such that<cmath>\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} +...")
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There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < … < a_k$ such that\[\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + … + 2^{a_k}.\]What is $k?$

$\textbf{(A) } 117 \qquad \textbf{(B) } 136 \qquad \textbf{(C) } 137 \qquad \textbf{(D) } 273 \qquad \textbf{(E) } 306$

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