Let $m \in \Bbb N$, $n \in \Bbb N$, such that $m$ divides $n$.
What is the output of a $DFT_m$ of order $m$ when the input is the coefficient vector of the polynomial $p(x) = x^n$?
Well this got me confused. I understand that $DFT$ is the output of doing $FFT$ method on a vector (or is it?) and it's more efficient than just multiplying $\left( O(n^2) \space vs \space O(n log n) \right)$
However I can't figure out this particular question.