Prove or disprove: L^2 context free implies L is context free
Hint. Let $U\subseteq\mathbb{N}$ be any undecidable set and let $I = \{2u+1\mid u\in U\} \cup \{0, 2, 4, \dots\}$. Let $L = \{a^i\mid i\in I\}$. Now prove that $L^2$&nbsp;is context-free but $L$&nbsp;is not.