{"status": "success", "data": {"description_md": "There exists a unique positive integer $a$ for which the sum $$U=\\sum_{n=1}^{2023}\\left\\lfloor\\dfrac{n^{2}-na}{5}\\right\\rfloor $$is an integer strictly between $-1000$ and $1000$. For that unique $a$, find $a+U$.<br><br>(Note that $\\lfloor x\\rfloor$ denotes the greatest integer that is 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>There exists a unique positive integer <span class=\"katex--inline\">a</span> for which the sum <span class=\"katex--display\">U=\\sum_{n=1}^{2023}\\left\\lfloor\\dfrac{n^{2}-na}{5}\\right\\rfloor</span>is an integer strictly between <span class=\"katex--inline\">-1000</span> and <span class=\"katex--inline\">1000</span>. For that unique <span class=\"katex--inline\">a</span>, find <span class=\"katex--inline\">a+U</span>.<br/><br/>(Note that <span class=\"katex--inline\">\\lfloor x\\rfloor</span> denotes the greatest integer that is 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": "2023 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_I_p11", "prev": "/problem/23_aime_I_p09"}}