{"status": "success", "data": {"description_md": "For how many positive integers $n$ less than or equal to $1000$ is $$(\\sin t + i \\cos t)^n=\\sin nt + i \\cos nt $$true for all real $t$?\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>For how many positive integers <span class=\"katex--inline\">n</span> less than or equal to <span class=\"katex--inline\">1000</span> is <span class=\"katex--display\">(\\sin t + i \\cos t)^n=\\sin nt + i \\cos nt</span>true for all real <span class=\"katex--inline\">t</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": "2005 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p10", "prev": "/problem/05_aime_II_p08"}}