Calculate \(\phi(54)\), \(\phi(540)\), and \(\phi(5400)\).

Show that if \(n\) is odd, then \(\phi(4n)=2 \phi(n)\).

Find four solutions of \(\phi(n)=16\).

Find all solutions of \(\phi(n)=4\) and prove that there are no more.

Show that \(\phi(n)=n/2\) if and only if \(n=2^k\) for some positive integer \(k\).

Show that \(\phi(n)=14\) is impossible.