{"status": "success", "data": {"description_md": "Find the number of positive integers $n$ less than $1000$ for which there exists a positive real number $x$ such that $n = x \\lfloor x \\rfloor$.<br>Note: $\\lfloor x \\rfloor$ is the greatest integer less than or equal to $x$.\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>Find the number of positive integers <span class=\"katex--inline\">n</span> less than <span class=\"katex--inline\">1000</span> for which there exists a positive real number <span class=\"katex--inline\">x</span> such that <span class=\"katex--inline\">n = x \\lfloor x \\rfloor</span>.<br/>Note: <span class=\"katex--inline\">\\lfloor x \\rfloor</span> is the greatest integer less than or equal to <span class=\"katex--inline\">x</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": "2012 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_II_p11", "prev": "/problem/12_aime_II_p09"}}