{"status": "success", "data": {"description_md": "For each positive integer $p$, let $b(p)$ denote the unique positive integer $k$ such that $|k-\\sqrt{p}|<\\frac{1}{2}$. For example, $b(6) = 2$ and $b(23)=5$. If $S = \\textstyle\\sum_{p=1}^{2007}b(p)$, 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>For each positive integer <span class=\"katex--inline\">p</span>, let <span class=\"katex--inline\">b(p)</span> denote the unique positive integer <span class=\"katex--inline\">k</span> such that <span class=\"katex--inline\">|k-\\sqrt{p}|&lt;\\frac{1}{2}</span>. For example, <span class=\"katex--inline\">b(6) = 2</span> and <span class=\"katex--inline\">b(23)=5</span>. If <span class=\"katex--inline\">S = \\textstyle\\sum_{p=1}^{2007}b(p)</span>, find the remainder when S is divided by 1000.</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": "2007 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/07_aime_I_p12", "prev": "/problem/07_aime_I_p10"}}