How could i show that $L=\{0^i | i \text{ is a perfect number} \}$ is not regular using pumping lemma?
1 Answer
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As far as I know, It is not known whether there are infinitely many perfect numbers, see here. As a result, if the number of perfect numbers are finite, $L$ is regular, of course. IMO, we otherwise need a lot of efforts to answer whether $L$ is regular or not, when knowing that perfect numbers are infinitely many.
