{"status": "success", "data": {"description_md": "Given that $z$ is a complex number such that $z+\\frac 1z=2\\cos 3^\\circ,$ find the least integer that is greater than $z^{2000}+\\frac 1{z^{2000}}.$\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>Given that <span class=\"katex--inline\">z</span> is a complex number such that <span class=\"katex--inline\">z+\\frac 1z=2\\cos 3^\\circ,</span> find the least integer that is greater than <span class=\"katex--inline\">z^{2000}+\\frac 1{z^{2000}}.</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": "2000 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_II_p10", "prev": "/problem/00_aime_II_p08"}}