Use the Pumping Lemma for Regular Languages to prove that this language is not regular:

$L=\{a^{n^3}|n>0\}.$ Use the string $s=a^{p^3}$ in your proof and cite Fermat's Last Theorem. Hint: Use Fermat's Last Theorem to choose a value for i that produces the contradiction.

a$.$ Start by stating the forms of $x,y,$ and $z.$

b$.$ Show the contradiction using condition $(1)$ of the PL$,$ i$.$e$.$ repeat the string $y.$