FiSGO.PIrrepsSearch.factorial_factor

factorial_factor(n, p)

An implementation of Legendre’s formula to compute the largest power of p dividing n!.

The formula is:

\[\nu_p(n!) = \sum_{i=1}^{\infty} \lfloor \frac{n}{p^{i}}\rfloor\]

Parameters:

• n (int) – value of n whose factorial is to be checked.

• p (int) – prime number.

Return type:

int

Returns:

the largest power of p that divides n!.