Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
So far I have: Base case (n = 1) = $8^{1} | (4(1))!$
= $8 | 24$ which is true.
Induction Step:
$8^{n + 1} | (4(n + 1))!$
$8^{n + 1} | (4n + 4)!$
- A bit confused as to how to close this proof out, also wanted to make sure my current progress is correct as well. Any help is appreciated.