I had came across a theorem a few weeks ago and I tried to make sense of it but could not at the time, so I put it down and recently picked it back up to take another shot, but the thing is, what I think this problem might involve I am not very familiar with in mathematical terms. I use it for programming when needed, being the (floor function) but not have had anything experiences mathematically. I would like to see how this problem is approached by mean of a mathematical induction but not literally "induction" if not needed.
The theorem is posed as so: $ \mathrm{e_p}(n!) = \sum_{r\ge 1} \! \left\lfloor\frac{n}{p^r}\right\rfloor $
Feel free to use any method, none in particular was in question of going about showing the above formula.
Thanks