{"status": "success", "data": {"description_md": "For how many positive integers $n$ does $1+2+...+n$ evenly divide $6n$? \n\n$\\mathrm{(A) \\ } 3\\qquad \\mathrm{(B) \\ } 5\\qquad \\mathrm{(C) \\ } 7\\qquad \\mathrm{(D) \\ } 9\\qquad \\mathrm{(E) \\ } 11$", "description_html": "<p>For how many positive integers  <span class=\"katex--inline\">n</span>  does  <span class=\"katex--inline\">1+2+...+n</span>  evenly divide  <span class=\"katex--inline\">6n</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 3\\qquad \\mathrm{(B) \\ } 5\\qquad \\mathrm{(C) \\ } 7\\qquad \\mathrm{(D) \\ } 9\\qquad \\mathrm{(E) \\ } 11</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 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p22", "prev": "/problem/05_amc10A_p20"}}