{"status": "success", "data": {"description_md": "Let $f$ be a function with the following properties:<br>(i) $f(1) = 1$, and<br>(ii) $f(2n) = n \\cdot f(n)$ for any positive integer $n$.<br>What is the value of $f(2^{100})$?\n\n$\\text {(A)}\\ 1 \\qquad \\text {(B)}\\ 2^{99} \\qquad \\text {(C)}\\ 2^{100} \\qquad \\text {(D)}\\ 2^{4950} \\qquad \\text {(E)}\\ 2^{9999}$\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>Let  <span class=\"katex--inline\">f</span>  be a function with the following properties:<br/>(i)  <span class=\"katex--inline\">f(1) = 1</span> , and<br/>(ii)  <span class=\"katex--inline\">f(2n) = n \\cdot f(n)</span>  for any positive integer  <span class=\"katex--inline\">n</span> .<br/>What is the value of  <span class=\"katex--inline\">f(2^{100})</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\text {(A)}\\ 1 \\qquad \\text {(B)}\\ 2^{99} \\qquad \\text {(C)}\\ 2^{100} \\qquad \\text {(D)}\\ 2^{4950} \\qquad \\text {(E)}\\ 2^{9999}</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": 3, "problem_name": "2004 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p18", "prev": "/problem/04_amc12A_p16"}}