{"status": "success", "data": {"description_md": "For each integer $n>1$, let $F(n)$ be the number of solutions to the equation $\\sin{x}=\\sin{(nx)}$ on the interval $[0,\\pi]$. What is $\\sum_{n=2}^{2007} F(n)$?<br>\t\n\n$\\mathrm{(A)}\\ 2014524 \\qquad \\mathrm{(B)}\\ 2015028 \\qquad \\mathrm{(C)}\\ 2015033 \\qquad \\mathrm{(D)}\\ 2016532 \\qquad \\mathrm{(E)}\\ 2017033$\n___\nFull 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 each integer  <span class=\"katex--inline\">n&gt;1</span> , let  <span class=\"katex--inline\">F(n)</span>  be the number of solutions to the equation  <span class=\"katex--inline\">\\sin{x}=\\sin{(nx)}</span>  on the interval  <span class=\"katex--inline\">[0,\\pi]</span> . What is  <span class=\"katex--inline\">\\sum_{n=2}^{2007} F(n)</span> ?<br/></p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 2014524 \\qquad \\mathrm{(B)}\\ 2015028 \\qquad \\mathrm{(C)}\\ 2015033 \\qquad \\mathrm{(D)}\\ 2016532 \\qquad \\mathrm{(E)}\\ 2017033</span> </p>&#10;<hr><p>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": 5, "problem_name": "2007 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p25", "prev": "/problem/07_amc12A_p23"}}