I have been trying to solve this question and am kinda stuck. Wondering on how to proceed and finish this proof. Prove that the language $ L = \{a^{2^n} | n >= 0\} $ is not regular. I have been trying to use the pumping lemma but am stuck at:
Suppose L were regular, let p be the pumping length given by the pumping lemma. $ w_p = 1^{2^n} $. Clearly, $ |w_p| >= p $ and $w_p$ is in L. So, by the pumping lemma, there must be some choice of x, y, z satisfying the conditions of the pumping lemma; $ |xy| <= n $ and $y > 0$.
I am stuck here, I do not how to proceed with solving the $(xy^iz)$ part.
Thanks
