{"status": "success", "data": {"description_md": "A set $S$ is constructed as follows. To begin, $S = \\{0,10\\}$. Repeatedly, as long as possible, if $x$ is an integer root of some polynomial $a_{n}x^n + a_{n-1}x^{n-1} + ... + a_{1}x + a_0$ for some $n\\geq{1}$, all of whose coefficients $a_i$ are elements of $S$, then $x$ is put into $S$. When no more elements can be added to $S$, how many elements does $S$ have?\n\n$\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad\\textbf{(C)}\\ 7 \\qquad\\textbf{(D)}\\ 9 \\qquad\\textbf{(E)}\\ 11$\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": "

A set S is constructed as follows. To begin, S = \\{0,10\\} . Repeatedly, as long as possible, if x is an integer root of some polynomial a_{n}x^n + a_{n-1}x^{n-1} + ... + a_{1}x + a_0 for some n\\geq{1} , all of whose coefficients a_i are elements of S , then x is put into S . When no more elements can be added to S , how many elements does S have?

\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad\\textbf{(C)}\\ 7 \\qquad\\textbf{(D)}\\ 9 \\qquad\\textbf{(E)}\\ 11

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": 5, "problem_name": "2017 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p22", "prev": "/problem/17_amc12A_p20"}}