{"status": "success", "data": {"description_md": "For each integer $n\\geq 4$, let $a_n$ denote the base-$n$ number $0.\\overline{133}_n$. The product $a_4a_5...a_{99}$ can be expressed as $\\frac {m}{n!}$, where $m$ and $n$ are positive integers and $n$ is as small as possible. What is the value of $m$?\n\n$\\text {(A) } 98 \\qquad \\text {(B) } 101 \\qquad \\text {(C) } 132\\qquad \\text {(D) } 798\\qquad \\text {(E) }962$\n___\nFull 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 integer  <span class=\"katex--inline\">n\\geq 4</span> , let  <span class=\"katex--inline\">a_n</span>  denote the base- <span class=\"katex--inline\">n</span>  number  <span class=\"katex--inline\">0.\\overline{133}_n</span> . The product  <span class=\"katex--inline\">a_4a_5...a_{99}</span>  can be expressed as  <span class=\"katex--inline\">\\frac {m}{n!}</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are positive integers and  <span class=\"katex--inline\">n</span>  is as small as possible. What is the value of  <span class=\"katex--inline\">m</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\text {(A) } 98 \\qquad \\text {(B) } 101 \\qquad \\text {(C) } 132\\qquad \\text {(D) } 798\\qquad \\text {(E) }962</span> </p>&#10;<hr><p>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": "2004 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/04_amc12A_p24"}}