Given a language $L = \left\{ a^{nk+1} | n > 0 \right\}$ and $k$ is an integer constant.
How to show that a DFA for this language must have $k+2$ states or more states using minimum state lemma.
By minimum state lemma I mean the number of minimum state a DFA has is the number of pairewise distinguishable states. I have constructed a set of pairewise distinguishable string ${a, aa, aaa, ... a^{k+2}}$ with respect to L and found that I can not add anymore strings to it. But I don't know how to prove this string has the maximum number of pairewise distinguishable strings.