{"status": "success", "data": {"description_md": "Let $P(x)$ be the unique polynomial of minimal degree with the following properties:\n*$P(x)$ has a leading coefficient $1$,\n*$1$ is a root of $P(x)-1$,\n*$2$ is a root of $P(x-2)$,\n*$3$ is a root of $P(3x)$, and\n*$4$ is a root of $4P(x)$.\nThe roots of $P(x)$ are integers, with one exception. The root that is not an integer can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers. What is $m+n$?\n\n$\\textbf{(A) }41\\qquad\\textbf{(B) }43\\qquad\\textbf{(C) }45\\qquad\\textbf{(D) }47\\qquad\\textbf{(E) }49$", "description_html": "

Let P(x) be the unique polynomial of minimal degree with the following properties:
\n* P(x) has a leading coefficient 1 ,
\n* 1 is a root of P(x)-1 ,
\n* 2 is a root of P(x-2) ,
\n* 3 is a root of P(3x) , and
\n* 4 is a root of 4P(x) .
\nThe roots of P(x) are integers, with one exception. The root that is not an integer can be written as \\frac{m}{n} , where m and n are relatively prime integers. What is m+n ?

\n

\\textbf{(A) }41\\qquad\\textbf{(B) }43\\qquad\\textbf{(C) }45\\qquad\\textbf{(D) }47\\qquad\\textbf{(E) }49

\n

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2023 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p22", "prev": "/problem/23_amc10A_p20"}}