{"status": "success", "data": {"description_md": "There is a polynomial $P(x)$ with integer coefficients such that $$P(x)=\\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)} $$holds for every $0<x<1.$ Find the coefficient of $x^{2022}$ in $P(x)$\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>There is a polynomial <span class=\"katex--inline\">P(x)</span> with integer coefficients such that <span class=\"katex--display\">P(x)=\\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}</span>holds for every <span class=\"katex--inline\">0&lt;x&lt;1.</span> Find the coefficient of <span class=\"katex--inline\">x^{2022}</span> in <span class=\"katex--inline\">P(x)</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": "2022 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_II_p14", "prev": "/problem/22_aime_II_p12"}}