I found an unanswered question on Math.SE concerning a footnote in an expository paper by Keith Conrad. It states that in general, the primitive th roots of unity in the th cyclotomic field form a normal basis over if and only if is squarefree.

The forward direction is not difficult to show. However, if is squarefree, then how can one show that the primitive th roots of unity form a basis for the cyclotomic extension over ?