Article ID Journal Published Year Pages File Type
4595095 Journal of Number Theory 2007 12 Pages PDF
Abstract

Consider the multiplicities ep1(n),ep2(n),…,epk(n) in which the primes p1,p2,…,pk appear in the factorization of n!. We show that these multiplicities are jointly uniformly distributed modulo (m1,m2,…,mk) for any fixed integers m1,m2,…,mk, thus improving a result of Luca and Stănică [F. Luca, P. Stănică, On the prime power factorization of n!, J. Number Theory 102 (2003) 298–305]. To prove the theorem, we obtain a result regarding the joint distribution of several completely q-additive functions, which seems to be of independent interest.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory