Let A be an arbitrary language over the one-letter alphabet "a". Prove A* is regular.
Partial Solution: If there are two strings in A* such that i and j are coprime then any a^K such that K > ij belongs to A*. Thus A* is regular.
But if i and j are not coprime, then... ?
Partial Solution: If there are two strings in A* such that i and j are coprime then any a^K such that K > ij belongs to A*. Thus A* is regular.
But if i and j are not coprime, then... ?