Let $x,y\in \{\frac{2\pi i}{2^m}\}_{0\leq i\leq 2^m-1 }$, where $m$ is a positive integer .
Q If we have that $\cos A=\cos x\cdot \cos y $, can we say that $A=\pi k$ for some $k\in \mathbb Q$.
For $m=1,2,3$, it is right. I do not know for the other cases.