{"status": "success", "data": {"description_md": "Ulquiorra finds a mysterious circle with radius $\\log_{2024}(a^{6})$. He then finds out that the circumference of the circle is $\\log_{2024}(b^{9})$. If $\\log_{b}(a)$ can be represented as $\\frac{m}{n\\pi}$, where $m$ and $n$ are positive relatively prime integers, what is $m+n$?", "description_html": "<p>Ulquiorra finds a mysterious circle with radius <span class=\"katex--inline\">\\log_{2024}(a^{6})</span>. He then finds out that the circumference of the circle is <span class=\"katex--inline\">\\log_{2024}(b^{9})</span>. If <span class=\"katex--inline\">\\log_{b}(a)</span> can be represented as <span class=\"katex--inline\">\\frac{m}{n\\pi}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are positive relatively prime integers, what is <span class=\"katex--inline\">m+n</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Holiday Contest 2025 - Guts Round - Set 1 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}