2012 AMC 12A Problems/Problem 25
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Problem
Let 
where 
denotes the fractional part of 
. The number 
is the smallest positive integer such that the equation ![\[nf(xf(x))=x\]](http://latex.artofproblemsolving.com/9/b/0/9b0829c5e8bdf5deb5dd048f42edb1d47bbbf0b5.png)
has at least 
real solutions. What is ? Note: the fractional part of is a real number 
such that 
and 
is an integer.
$\textbf{(A)}\ 30\qquad\textbf{(B)}\ 31\qquad\textbf{(C)}\ 32\qquad\textbf{(D)}\ 62\qquad\textbf{(E)}\64$ (Error compiling LaTeX. Unknown error_msg)
Solution
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