OBM 1987 Problem 1

$p(x_1, x_2, ... , x_n)$ is a polynomial with integer coefficients. For each positive integer $r, k(r)$ is the number of $n$ -tuples $(a_1, a_2,... , a_n)$ such that $0 \le a_i \le r-1$ and $p(a_1, a_2, ... , a_n)$ 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 $k(p^s) = p^{n(s-1)} k(p)$ .