{"status": "success", "data": {"description_md": "Let $m$ be a positive integer, and let $a_0, a_1,\\ldots,a_m$ be a sequence of reals such that $a_0=37$, $a_1=72$, $a_m=0$, and $$a_{k+1}=a_{k-1}-\\frac{3}{a_k} $$for $k=1,2, \\ldots, m-1$. Find $m$.\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\">m</span> be a positive integer, and let <span class=\"katex--inline\">a_0, a_1,\\ldots,a_m</span> be a sequence of reals such that <span class=\"katex--inline\">a_0=37</span>, <span class=\"katex--inline\">a_1=72</span>, <span class=\"katex--inline\">a_m=0</span>, and <span class=\"katex--display\">a_{k+1}=a_{k-1}-\\frac{3}{a_k}</span>for <span class=\"katex--inline\">k=1,2, \\ldots, m-1</span>. Find <span class=\"katex--inline\">m</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": "2005 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p12", "prev": "/problem/05_aime_II_p10"}}