Let the positive integer $n$ be written as powers of prime $p$ so that we have $n=a_kp^k+....+a_2p^2+a_1p+a_0,$ where $0\leq a_i
I know that the exponent of $p$ in $n!$ is $\sum_{k=1}^{\infty}\left\lfloor\frac{n}{p^k}\right\rfloor$. But I got stuck on how to use the given expression of $n$. Any suggestions?
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