Can anyone provide a proof of the equidistribution theorem using Weyl's criterion for the case of $c*a \,\,\, \text{(mod 1)}$ where $c=2^n: \,\,\, \forall n \in W$$c=2^n: \,\,\, \forall n \in N_0$ for irrational algebraic $a$? The original equidistribution theorem is for the case that $c = n: \,\,\, \forall n \in W$$c = n: \,\,\, \forall n \in N_0$. Much thanks in advance.