{"status": "success", "data": {"description_md": "Let $a=\\pi/2008$. Find the smallest positive integer $n$ such that\n$$ 2[\\cos(a)\\sin(a)+\\cos(4a)\\sin(2a)+\\cos(9a)\\sin(3a)+\\cdots+\\cos(n^2a)\\sin(na)] $$ is an integer.\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\">a=\\pi/2008</span>. Find the smallest positive integer <span class=\"katex--inline\">n</span> such that<br/>&#10;<span class=\"katex--display\"> 2[\\cos(a)\\sin(a)+\\cos(4a)\\sin(2a)+\\cos(9a)\\sin(3a)+\\cdots+\\cos(n^2a)\\sin(na)] </span> is an integer.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2008 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p09", "prev": "/problem/08_aime_II_p07"}}