{"status": "success", "data": {"description_md": "For certain pairs $(m,n)$ of positive integers with $m\\ge n$ there are exactly $50$ distinct positive integers $k$ such that $|\\log m - \\log k| < \\log n$. Find the sum of all possible values of the product $mn$.\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>For certain pairs <span class=\"katex--inline\">(m,n)</span> of positive integers with <span class=\"katex--inline\">m\\ge n</span> there are exactly <span class=\"katex--inline\">50</span> distinct positive integers <span class=\"katex--inline\">k</span> such that <span class=\"katex--inline\">|\\log m - \\log k| &lt; \\log n</span>. Find the sum of all possible values of the product <span class=\"katex--inline\">mn</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2009 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p12", "prev": "/problem/09_aime_II_p10"}}