{"status": "success", "data": {"description_md": "The terms of the sequence $(a_i)$ defined by $a_{n + 2} = \\frac {a_n + 2009} {1 + a_{n + 1}}$ for $n \\ge 1$ are positive integers. Find the minimum possible value of $a_1 + a_2$.\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 terms of the sequence <span class=\"katex--inline\">(a_i)</span> defined by <span class=\"katex--inline\">a_{n + 2} = \\frac {a_n + 2009} {1 + a_{n + 1}}</span> for <span class=\"katex--inline\">n \\ge 1</span> are positive integers. Find the minimum possible value of <span class=\"katex--inline\">a_1 + a_2</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": 6, "problem_name": "2009 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_I_p14", "prev": "/problem/09_aime_I_p12"}}