Thursday, May 3, 2018

elementary number theory - the exponent of the highest power of p dividing n!

The formula for the exponent of the highest power of prime $p$ dividing $n!$ is $\sum \frac{n}{p^k}$, but the question is $n=1000!$ (really, it has the factorial) and $p=5$.


When I use Wolfram Alpha , I panicked because the number has $2,567$ decimal digits.


I think if I write this number I'd need paper all the way to the Amazon.


Perhaps I misunderstand the formula?

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