{"status": "success", "data": {"description_md": "Let a sequence be defined as follows: $a_{1}= 3$, $a_{2}= 3$, and for $n \\ge 2$, $a_{n+1}a_{n-1}= a_{n}^{2}+2007$. Find the largest integer less than or equal to $\\frac{a_{2007}^{2}+a_{2006}^{2}}{a_{2007}a_{2006}}$.\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": "

Let a sequence be defined as follows: a_{1}= 3, a_{2}= 3, and for n \\ge 2, a_{n+1}a_{n-1}= a_{n}^{2}+2007. Find the largest integer less than or equal to \\frac{a_{2007}^{2}+a_{2006}^{2}}{a_{2007}a_{2006}}.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2007 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/07_aime_I_p15", "prev": "/problem/07_aime_I_p13"}}