{"status": "success", "data": {"description_md": "Let the expression $\\dfrac{(5^4 + \\frac{1}{4})(7^4 + \\frac{1}{4})(9^4 + \\frac{1}{4})(11^4 + \\frac{1}{4})(13^4 + \\frac{1}{4})}{(4^4 + \\frac{1}{4})(6^4 + \\frac{1}{4})(8^4 + \\frac{1}{4})(10^4 + \\frac{1}{4})(12^4 + \\frac{1}{4})} = \\dfrac{m}{n}$, where $m$ and $n$ $\\in \\mathbb{Z}^+$ and $\\gcd(m, n) = 1$. Compute $m + n$.", "description_html": "<p>Let the expression <span class=\"katex--inline\">\\dfrac{(5^4 + \\frac{1}{4})(7^4 + \\frac{1}{4})(9^4 + \\frac{1}{4})(11^4 + \\frac{1}{4})(13^4 + \\frac{1}{4})}{(4^4 + \\frac{1}{4})(6^4 + \\frac{1}{4})(8^4 + \\frac{1}{4})(10^4 + \\frac{1}{4})(12^4 + \\frac{1}{4})} = \\dfrac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> <span class=\"katex--inline\">\\in \\mathbb{Z}^+</span> and <span class=\"katex--inline\">\\gcd(m, n) = 1</span>. Compute <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Christmas Contest - Guts Round - Set 7 Problem 1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}