{"status": "success", "data": {"description_md": "Let $f$ be a function with the following properties:\n\n$(\\text{i})\\;\\;$ $f(1) = 1$, and\n$(\\text{ii})\\;$ $f(2n) = n \\cdot f(n)$ for any positive integer $n$.\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:</p>&#10;<p><span class=\"katex--inline\">(\\text{i})\\;\\;</span> <span class=\"katex--inline\">f(1) = 1</span>, and<br/>&#10;<span class=\"katex--inline\">(\\text{ii})\\;</span> <span class=\"katex--inline\">f(2n) = n \\cdot f(n)</span> for any positive integer <span class=\"katex--inline\">n</span>.</p>&#10;<p>What is the value of <span class=\"katex--inline\">f(2^{100})</span>?</p>&#10;<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>&#10;", "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"}}