Shrey Jha

p-adic Valuations of Generalized Multifactorials: A Legendre-Type Formula

The classical Legendre formula expresses the p-adic valuation of the factorial n! in terms of the base-p digit sum of n. We generalize this result to the α-th order multifactorial, the product of n and every α-th integer below it, for arbitrary integers α at least 2. When α divid...