{"status": "success", "data": {"description_md": "The number $$ \\frac 2{\\log_4{2000^6}}+\\frac 3{\\log_5{2000^6}} $$ can be written as $\\frac mn$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\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>The number <span class=\"katex--display\"> \\frac 2{\\log_4{2000^6}}+\\frac 3{\\log_5{2000^6}} </span> can be written as <span class=\"katex--inline\">\\frac mn</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m+n.</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2000 AIME II Problem 1", "can_next": true, "can_prev": false, "nxt": "/problem/00_aime_II_p02", "prev": ""}}