Half Factorial

Prove : For any positive integers p, k,
$latex (p^k)! text { is divisible by p }$
Proof:
Apply Factorial Formula:
$latex boxed {n!=n.(n-1)! } $

$latex (p^k)! = (p^k). (p^k -1)!
= p.(p^{k-1}).(p^k -1)!
$
hence divisible by p. [QED]