{"status": "success", "data": {"description_md": "Call a set $S$ product-free if there do not exist $a, b, c \\in S$ (not necessarily distinct) such that $a b = c$. For example, the empty set and the set $\\{16, 20\\}$ are product-free, whereas the sets $\\{4, 16\\}$ and $\\{2, 8, 16\\}$ are not product-free. Find the number of product-free subsets of the set $\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}$.\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>Call a set <span class=\"katex--inline\">S</span> product-free if there do not exist <span class=\"katex--inline\">a, b, c \\in S</span> (not necessarily distinct) such that <span class=\"katex--inline\">a b = c</span>. For example, the empty set and the set <span class=\"katex--inline\">\\{16, 20\\}</span> are product-free, whereas the sets <span class=\"katex--inline\">\\{4, 16\\}</span> and <span class=\"katex--inline\">\\{2, 8, 16\\}</span> are not product-free. Find the number of product-free subsets of the set <span class=\"katex--inline\">\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}</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": "2017 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/17_aime_I_p13", "prev": "/problem/17_aime_I_p11"}}