## A prime $p$ doesn’t divide $\dbinom{p^am}{p^a}$

Let $$p$$ be a prime, and $$(a,m)\in{\Bbb{N}^2}$$ with $$\gcd(p,m)=1$$. Then $$p$$ doesn’t divide $$\dbinom{p^am}{p^a}$$.

I need this to prove the existence Sylow theorem. I don’t really know how to proceed.