{"status": "success", "data": {"description_md": "Let $f$ be a function with the following properties:\n(i) $f(1) = 1$, and\n(ii) $f(2n) = n \\cdot f(n)$ for any positive integer $n$.\nWhat is the value of $f(2^{100})$?\n\n$\\mathrm{(A) \\ } 1 \\qquad \\mathrm{(B) \\ } 2^{99} \\qquad \\mathrm{(C) \\ } 2^{100} \\qquad \\mathrm{(D) \\ } 2^{4950} \\qquad \\mathrm{(E) \\ } 2^{9999}$", "description_html": "<p>Let  <span class=\"katex--inline\">f</span>  be a function with the following properties:<br/>\n(i)  <span class=\"katex--inline\">f(1) = 1</span> , and<br/>\n(ii)  <span class=\"katex--inline\">f(2n) = n \\cdot f(n)</span>  for any positive integer  <span class=\"katex--inline\">n</span> .<br/>\nWhat is the value of  <span class=\"katex--inline\">f(2^{100})</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 1 \\qquad \\mathrm{(B) \\ } 2^{99} \\qquad \\mathrm{(C) \\ } 2^{100} \\qquad \\mathrm{(D) \\ } 2^{4950} \\qquad \\mathrm{(E) \\ } 2^{9999}</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": "2004 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p25", "prev": "/problem/04_amc10A_p23"}}