{"status": "success", "data": {"description_md": "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 all elements in $R$. Find the remainder when $S$ is divided by $1000$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let <span class=\"katex--inline\">R</span> be the set of all possible remainders when a number of the form <span class=\"katex--inline\">2^n</span>, <span class=\"katex--inline\">n</span> a nonnegative integer, is divided by <span class=\"katex--inline\">1000</span>. Let <span class=\"katex--inline\">S</span> be the sum of all elements in <span class=\"katex--inline\">R</span>. Find the remainder when <span class=\"katex--inline\">S</span> is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2011 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_I_p12", "prev": "/problem/11_aime_I_p10"}}