{"status": "success", "data": {"description_md": "The sets $A = \\{z : z^{18} = 1\\}$ and $B = \\{w : w^{48} = 1\\}$ are both sets of complex roots of unity. The set $C = \\{zw : z \\in A \\ \\text{and} \\ w \\in B\\}$ is also a set of complex roots of unity. How many distinct elements are in $C$?\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>The sets <span class=\"katex--inline\">A = \\{z : z^{18} = 1\\}</span> and <span class=\"katex--inline\">B = \\{w : w^{48} = 1\\}</span> are both sets of complex roots of unity. The set <span class=\"katex--inline\">C = \\{zw : z \\in A \\ \\text{and} \\ w \\in B\\}</span> is also a set of complex roots of unity. How many distinct elements are in <span class=\"katex--inline\">C</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": 5, "problem_name": "1990 AIME Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/90_aime_p11", "prev": "/problem/90_aime_p09"}}