Question 5
$p(x_1, x_2, \dots, x_n)$ is a polynomial with integer coefficients. For each positive integer $r$, $k(r)$ is the number of $n$-tuples $(a_1, a_2, \dots, a_n)$ such that $0 \le a_i \le r - 1$ and $p(a_1, a_2, \dots, a_n)$ is prime to $r$. Show that if $u$ and $v$ are coprime then $k(u \cdot v) = k(u) \cdot k(v)$, and if $p$ is prime then $k(p^s) = p^{n(s-1)}k(p)$.