Is there always a solution to the following equation: $$e^{\frac{2i\pi}{2^m}} \cdot e^{\frac{2i \pi w}{2^n}} = \sum_{k=-(m+n)}^{m+n} {b_k \cdot e^{\frac{2 i \pi}{2^k}}}$$
with $m,n,w,b_k$ being integers?
If there is, how do you find $b_k$ in terms of $m,n,w$ and $k$?
This is important for the Fast Fourier Transform, as I have developed a specific algorithm that hinges solely on this property. I would be very glad if there was such an identity for $b_k$, or if anyone could prove there isn't such a thing .