{"status": "success", "data": {"description_md": "**POTD April 5, 2024**\n\nLet $r, s,$ and $t$ be the distinct roots of $x^3 -2022x^2 + 2022x + 2022.$ If $\\frac{1}{r^2-1}+\\frac{1}{s^2-1}+\\frac{1}{t^2-1}$ can be expressed as $-\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers,find $m+n.$", "description_html": "<p><strong>POTD April 5, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">r, s,</span> and <span class=\"katex--inline\">t</span> be the distinct roots of <span class=\"katex--inline\">x^3 -2022x^2 + 2022x + 2022.</span> If <span class=\"katex--inline\">\\frac{1}{r^2-1}+\\frac{1}{s^2-1}+\\frac{1}{t^2-1}</span> can be expressed as <span class=\"katex--inline\">-\\frac{m}{n},</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers,find <span class=\"katex--inline\">m+n.</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #118", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}