12) Suppose that $p \ge 3$ is an odd prime and $n \ge 3$ is an odd integer.
a. Suppose that $g$ and $g'$ are both primitive roots modulo $p$. Show that $gg'$ is not a primitive root
modulo $p$.
b. Suppose that $g_1, g_2, \dots, g_s$ are the primitive roots modulo $p$. Show that
$g_1 g_2 \dots g_s \equiv 1 \pmod{p}$.
c. Suppose that $h_1, h_2, \dots, h_s$ are the primitive roots modulo $n$. Does your proof for b) show that
$h_1 h_2 \dots h_s \equiv 1 \pmod{n}$? If not, where does the proof fail?
