{"status": "success", "data": {"description_md": "Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$, and $\\left(P(2)\\right)^2 = P(3)$. Then $P(\\tfrac72)=\\tfrac{m}{n}$, 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>Let <span class=\"katex--inline\">P(x)</span> be a nonzero polynomial such that <span class=\"katex--inline\">(x-1)P(x+1)=(x+2)P(x)</span> for every real <span class=\"katex--inline\">x</span>, and <span class=\"katex--inline\">\\left(P(2)\\right)^2 = P(3)</span>. Then <span class=\"katex--inline\">P(\\tfrac72)=\\tfrac{m}{n}</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><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": "2016 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_I_p12", "prev": "/problem/16_aime_I_p10"}}