{"status": "success", "data": {"description_md": "For how many integers $n$ is $72\\left(\\frac{3}{2}\\right)^n$ equal to an integer?\n\n$\\text{(A)}\\ 2\\qquad\\text{(B)}\\ 3\\qquad\\text{(C)}\\ 4\\qquad\\text{(D)}\\ 5\\qquad\\text{(E)}\\ 6$\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 how many integers <span class=\"katex--inline\">n</span> is <span class=\"katex--inline\">72\\left(\\frac{3}{2}\\right)^n</span> equal to an integer?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 2\\qquad\\text{(B)}\\ 3\\qquad\\text{(C)}\\ 4\\qquad\\text{(D)}\\ 5\\qquad\\text{(E)}\\ 6</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": 2, "problem_name": "2015 Cayley Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p21", "prev": "/problem/15_cayley_p19"}}