16. a) Show that if $p$ and $q$ are distinct odd primes, then $p q$ is a pseudoprime to the base 2 if and only if $\operatorname{ord}_{q} 2 \mid(p-1)$ and $\operatorname{ord}_{p} 2 \mid(q-1)$.
b) Use part (a) to decide which of the following integers are pseudoprimes to the base 2: $13 \cdot 67,19 \cdot 73,23 \cdot 89,29 \cdot 97$.