{"status": "success", "data": {"description_md": "For how many integers $n$ between $1$ and $50$, inclusive, is\n\n$$\\frac{(n^2-1)!}{(n!)^n}$$<br>an integer? (Recall that $0! = 1$.)\n\n$\\textbf{(A) } 31 \\qquad \\textbf{(B) } 32 \\qquad \\textbf{(C) } 33 \\qquad \\textbf{(D) } 34 \\qquad \\textbf{(E) } 35$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For how many integers  <span class=\"katex--inline\">n</span>  between  <span class=\"katex--inline\">1</span>  and  <span class=\"katex--inline\">50</span> , inclusive, is</p>&#10;<p> <span class=\"katex--display\">\\frac{(n^2-1)!}{(n!)^n}</span> <br/>an integer? (Recall that  <span class=\"katex--inline\">0! = 1</span> .)</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 31 \\qquad \\textbf{(B) } 32 \\qquad \\textbf{(C) } 33 \\qquad \\textbf{(D) } 34 \\qquad \\textbf{(E) } 35</span> </p>&#10;<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": 5, "problem_name": "2019 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p25", "prev": "/problem/19_amc12A_p23"}}