By definition, the positive integers that have a primitive root are 2, 4 and integers of the form $\displaystyle p^t$ and $\displaystyle 2p^t$ where p is a prime and t is a positive integer.

Then why does 16 NOT have a primitive root? $\displaystyle 16 = 2^4$ and 2 is prime and 4 is a positive integer.

I'm confused...