The Legendre's formula for the p-adic valuation of a factorial | number theory | intermediate level

Episode 131.

The Legendre's formula for the p-adic valuation of a factorial | number theory | intermediate level.

Branch of mathematics: general mathematics.
Difficulty level: intermediate.

Theorem. For any $n$ and any prime number $p$, we have $\nu_p(n!) = \sum_{k=1}^{\infty}{\left\lfloor \frac{n}{p^k} \right\rfloor}$.

Mathematics. Number theory.
#Mathematics #NumberTheory

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