{"status": "success", "data": {"description_md": "For how many positive integers $n$ less than or equal to $24$ is $n!$ evenly divisible by $1 + 2 + \\ldots + n$?\n\n$\\mathrm{(A)} 8 \\qquad \\mathrm{(B)} 12 \\qquad \\mathrm{(C)} 16 \\qquad \\mathrm{(D)} 17 \\qquad \\mathrm{(E)} 21$", "description_html": "<p>For how many positive integers  <span class=\"katex--inline\">n</span>  less than or equal to  <span class=\"katex--inline\">24</span>  is  <span class=\"katex--inline\">n!</span>  evenly divisible by  <span class=\"katex--inline\">1 + 2 + \\ldots + n</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} 8 \\qquad \\mathrm{(B)} 12 \\qquad \\mathrm{(C)} 16 \\qquad \\mathrm{(D)} 17 \\qquad \\mathrm{(E)} 21</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2005 AMC 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10B_p23", "prev": "/problem/05_amc10B_p21"}}