2013 AMC 12B Problems/Problem 25
Problem
Let 
be the set of polynomials of the form
![\[P(z)=z^n+c_{n-1}z^{n-1}+\cdots+c_2z^2+c_1z+50,\]](http://latex.artofproblemsolving.com/3/d/e/3de0be2f12d213af5652e01e8167c9cf06b89ef9.png)
where 
are integers and 
has distinct roots of the form 
with 
and 
integers. How many polynomials are in ?
$\textbf{(A)}\ 288\qquad\textbf{(B)}\ 528\qquad\textbf{(C)}\ 576\qquad\textbf{(D}}\ 992\qquad\textbf{(E)}\ 1056$ (Error compiling LaTeX. Unknown error_msg)
