{"status": "success", "data": {"description_md": "Let $P(x)$ be a polynomial with integer coefficients that satisfies $P(17)=10$ and $P(24)=17$. Given that $P(n)=n+3$ has two distinct integer solutions $n_1$ and $n_2$, find the product $n_1\\cdot n_2$.\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>Let <span class=\"katex--inline\">P(x)</span> be a polynomial with integer coefficients that satisfies <span class=\"katex--inline\">P(17)=10</span> and <span class=\"katex--inline\">P(24)=17</span>. Given that <span class=\"katex--inline\">P(n)=n+3</span> has two distinct integer solutions <span class=\"katex--inline\">n_1</span> and <span class=\"katex--inline\">n_2</span>, find the product <span class=\"katex--inline\">n_1\\cdot n_2</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": 6, "problem_name": "2005 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p14", "prev": "/problem/05_aime_II_p12"}}