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2011 AIME I Problems/Problem 11

Revision as of 11:56, 19 March 2011 by AlphaMath1 (talk | contribs) (Created page with '== Problem == Let <math>R</math> be the set of all possible remainders when a number of the form <math>2^n</math>, <math>n</math> a nonnegative integer, is divided by <math>1000<…')
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Problem

Let $R$ be the set of all possible remainders when a number of the form $2^n$, $n$ a nonnegative integer, is divided by $1000$. Let $S$ be the sum of the elements in $R$. Find the remainder when $S$ is divided by $1000$.

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