{"status": "success", "data": {"description_md": "Let $ M \\ge 3$ be an integer and let $ S = \\{3,4,5,\\ldots,m\\}$. Find the smallest value of $ m$ such that for every partition of $ S$ into two subsets, at least one of the subsets contains integers $ a$, $ b$, and $ c$ (not necessarily distinct) such that $ ab = c$.<br><br>Note: a partition of $ S$ is a pair of sets $ A$, $ B$ such that $ A \\cap B = \\emptyset$, $ A \\cup B = S$.\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 $ M \\ge 3$ be an integer and let $ S = {3,4,5,\\ldots,m}$. Find the smallest value of $ m$ such that for every partition of $ S$ into two subsets, at least one of the subsets contains integers $ a$, $ b$, and $ c$ (not necessarily distinct) such that $ ab = c$.<br/><br/>Note: a partition of $ S$ is a pair of sets $ A$, $ B$ such that $ A \\cap B = \\emptyset$, $ A \\cup B = S$.</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": "2010 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_I_p13", "prev": "/problem/10_aime_I_p11"}}