{"status": "success", "data": {"description_md": "Suppose that $\\dfrac{2009}{2014} + \\dfrac{2019}{n} = \\dfrac{a}{b}$, where $a$, $b$ and $n$ are positive integers with $\\dfrac{a}{b}$ in lowest terms. What is the sum of the digits of the smallest positive integer $n$ for which $a$ is a multiple of 1004?\n\n$\\text{(A)}\\ 16\\qquad\\text{(B)}\\ 17\\qquad\\text{(C)}\\ 14\\qquad\\text{(D)}\\ 20\\qquad\\text{(E)}\\ 21$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>Suppose that <span class=\"katex--inline\">\\dfrac{2009}{2014} + \\dfrac{2019}{n} = \\dfrac{a}{b}</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> and <span class=\"katex--inline\">n</span> are positive integers with <span class=\"katex--inline\">\\dfrac{a}{b}</span> in lowest terms. What is the sum of the digits of the smallest positive integer <span class=\"katex--inline\">n</span> for which <span class=\"katex--inline\">a</span> is a multiple of 1004?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 16\\qquad\\text{(B)}\\ 17\\qquad\\text{(C)}\\ 14\\qquad\\text{(D)}\\ 20\\qquad\\text{(E)}\\ 21</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Pascal</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 Pascal Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/14_pascal_p24"}}