{"status": "success", "data": {"description_md": "For every $m \\geq 2$, let $Q(m)$ be the least positive integer with the following property: For every $n \\geq Q(m)$, there is always a perfect cube $k^3$ in the range $n < k^3 \\leq m \\cdot n$. Find the remainder when<br>\n$$ \\sum_{m = 2}^{2017} Q(m) $$is divided by 1000.\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 every <span class=\"katex--inline\">m \\geq 2</span>, let <span class=\"katex--inline\">Q(m)</span> be the least positive integer with the following property: For every <span class=\"katex--inline\">n \\geq Q(m)</span>, there is always a perfect cube <span class=\"katex--inline\">k^3</span> in the range <span class=\"katex--inline\">n &lt; k^3 \\leq m \\cdot n</span>. Find the remainder when<br/><span class=\"katex--display\"> \\sum_{m = 2}^{2017} Q(m) </span>is divided by 1000.</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": 6, "problem_name": "2017 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/17_aime_I_p14", "prev": "/problem/17_aime_I_p12"}}