{"status": "success", "data": {"description_md": "Find the number of ordered pairs $(m, n)$ such that $m$ and $n$ are positive integers in the set $\\{1, 2, ..., 30\\}$ and the greatest common divisor of $2^m + 1$ and $2^n - 1$ is not $1.$\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>Find the number of ordered pairs <span class=\"katex--inline\">(m, n)</span> such that <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are positive integers in the set <span class=\"katex--inline\">\\{1, 2, ..., 30\\}</span> and the greatest common divisor of <span class=\"katex--inline\">2^m + 1</span> and <span class=\"katex--inline\">2^n - 1</span> is not <span class=\"katex--inline\">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": 4, "problem_name": "2021 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p10", "prev": "/problem/21_aime_II_p08"}}