{"status": "success", "data": {"description_md": "There are $24$ different complex numbers $z$ such that $z^{24}=1$. For how many of these is $z^6$ a real number?\n\n$\\textbf{(A)}\\ 0 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 6 \\qquad\\textbf{(D)}\\ 12 \\qquad\\textbf{(E)}\\ 24$\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>There are  <span class=\"katex--inline\">24</span>  different complex numbers  <span class=\"katex--inline\">z</span>  such that  <span class=\"katex--inline\">z^{24}=1</span> . For how many of these is  <span class=\"katex--inline\">z^6</span>  a real number?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 0 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 6 \\qquad\\textbf{(D)}\\ 12 \\qquad\\textbf{(E)}\\ 24</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": 3, "problem_name": "2017 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p18", "prev": "/problem/17_amc12A_p16"}}