{"status": "success", "data": {"description_md": "The polynomial $f(z)=az^{2018}+bz^{2017}+cz^{2016}$ has real coefficients not exceeding $2019$, and $f(\\tfrac{1+\\sqrt{3}i}{2})=2015+2019\\sqrt{3}i$. Find the remainder when $f(1)$ is divided by $1000$.\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 polynomial <span class=\"katex--inline\">f(z)=az^{2018}+bz^{2017}+cz^{2016}</span> has real coefficients not exceeding <span class=\"katex--inline\">2019</span>, and <span class=\"katex--inline\">f(\\tfrac{1+\\sqrt{3}i}{2})=2015+2019\\sqrt{3}i</span>. Find the remainder when <span class=\"katex--inline\">f(1)</span> is divided by <span class=\"katex--inline\">1000</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": 4, "problem_name": "2019 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p09", "prev": "/problem/19_aime_II_p07"}}