Show that the language is regular

Question

Let $$B_n=\{a^k \ \mid \ k \text{ is a multiple of } n\}$$

Show that for each $n \geq 1$, the language $B_n$ is regular.

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Could you give me some hints how we coukd show this??

Do we have to construct a NFA that accepts this language??

Answer 1

Hint:

• If $a^n$ was a single letter, say $\alpha$, then $B_n$ could be represented by regular expression $\alpha^*$.

I hope this helps $\ddot\smile$