{"status": "success", "data": {"description_md": "For each positive integer $n$, define $S(n)$ to be the smallest positive integer divisible by each of the positive integers $1, 2, 3, \\ldots, n$. For example, $S(5) = 60$. How many positive integers $n$ with $1 \\leq n \\leq 100$ have $S(n) = S(n+4)$?\n\n$\\text{(A)}\\ 9\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 12\\qquad\\text{(E)}\\ 13$\n\n___\n\n**[Cayley](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>For each positive integer <span class=\"katex--inline\">n</span>, define <span class=\"katex--inline\">S(n)</span> to be the smallest positive integer divisible by each of the positive integers <span class=\"katex--inline\">1, 2, 3, \\ldots, n</span>. For example, <span class=\"katex--inline\">S(5) = 60</span>. How many positive integers <span class=\"katex--inline\">n</span> with <span class=\"katex--inline\">1 \\leq n \\leq 100</span> have <span class=\"katex--inline\">S(n) = S(n+4)</span>?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 9\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 12\\qquad\\text{(E)}\\ 13</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</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 Cayley Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/14_cayley_p25", "prev": "/problem/14_cayley_p23"}}