{"status": "success", "data": {"description_md": "Let $f$ be a function from the positive reals to the positive reals such that $xf(xf(2y)) = y+xyf(x)$ for all $x$ and $y$ in the domain. If the sum of all values of $f(100)$ can be written as $\\frac{m}{n}$, where $\\gcd(m,n) = 1$, find $m+n$.", "description_html": "<p>Let <span class=\"katex--inline\">f</span> be a function from the positive reals to the positive reals such that <span class=\"katex--inline\">xf(xf(2y)) = y+xyf(x)</span> for all <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> in the domain. If the sum of all values of <span class=\"katex--inline\">f(100)</span> can be written as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">\\gcd(m,n) = 1</span>, 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": "AMC Practice #1 - Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/amc1-p14", "prev": "/problem/amc1-p12"}}