{"status": "success", "data": {"description_md": "For each positive integer $n > 1$, let $P(n)$ denote the greatest prime factor of $n$. For how many positive integers $n$ is it true that both $P(n) = \\sqrt{n}$ and $P(n+48) = \\sqrt{n+48}$?\n\n$\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 3\\qquad \\mathrm{(D) \\ } 4\\qquad \\mathrm{(E) \\ } 5$", "description_html": "<p>For each positive integer  <span class=\"katex--inline\">n &gt; 1</span> , let  <span class=\"katex--inline\">P(n)</span>  denote the greatest prime factor of  <span class=\"katex--inline\">n</span> . For how many positive integers  <span class=\"katex--inline\">n</span>  is it true that both  <span class=\"katex--inline\">P(n) = \\sqrt{n}</span>  and  <span class=\"katex--inline\">P(n+48) = \\sqrt{n+48}</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 3\\qquad \\mathrm{(D) \\ } 4\\qquad \\mathrm{(E) \\ } 5</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 24", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p25", "prev": "/problem/05_amc10A_p23"}}