{"status": "success", "data": {"description_md": "For each positive integer $n$ let $a_n$ be the least positive integer multiple of $23$ such that $a_n\\equiv1\\pmod{2^n}$. Find the number of positive integers $n$ less than or equal to $1000$ that satisfy $a_n=a_{n+1}$.\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 each positive integer <span class=\"katex--inline\">n</span> let <span class=\"katex--inline\">a_n</span> be the least positive integer multiple of <span class=\"katex--inline\">23</span> such that <span class=\"katex--inline\">a_n\\equiv1\\pmod{2^n}</span>. Find the number of positive integers <span class=\"katex--inline\">n</span> less than or equal to <span class=\"katex--inline\">1000</span> that satisfy <span class=\"katex--inline\">a_n=a_{n+1}</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": 6, "problem_name": "2023 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/23_aime_II_p14"}}