{"status": "success", "data": {"description_md": "Let $A$ be an acute angle such that $\\tan A = 2\\cos A$. Find the number of positive integers $n$ less than or equal to $1000$ such that $\\sec^n A + \\tan^n A$ is a positive integer whose units digit is $9$.\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>Let <span class=\"katex--inline\">A</span> be an acute angle such that <span class=\"katex--inline\">\\tan A = 2\\cos A</span>. Find the number of positive integers <span class=\"katex--inline\">n</span> less than or equal to <span class=\"katex--inline\">1000</span> such that <span class=\"katex--inline\">\\sec^n A + \\tan^n A</span> is a positive integer whose units digit is <span class=\"katex--inline\">9</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 13", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_II_p14", "prev": "/problem/23_aime_II_p12"}}