So I have a language: $$ L = \{a^{n^2} \mid n > 0\} $$ I need to prove that this language isn't context-free using the pumping lemma. I have a vague thought process as to how to do the proof but I'm sort of doubting its validity.
So I take a pumping length $p$ such that a word $a^{p^2}$ can be split into 5 parts $uvxyz$. I need to assume that $L$ is context-free and run through some cases and check if the word violates the pumping lemma or if it doesn't violate the pumping lemma but isn't in the language definition.
I know the concept of proving languages aren't context free and the pumping lemma but I'm very stuck applying it to this particular language.
What do I do?