Regularity of patterns in the factorization of n!
The authors consider the multiplicities \(e_{p_1}(n),\dots,e_{p_k}(n)\) in which the primes \(p_1,\dots,p_k\) appear in the factorization of \(n\)! It is proved that these multiplicities are jointly uniformly distributed modulo \((m_1,m_2,\dots,m_k)\) for any fixed integers \(m_1,\dots,m_k\), thus improving \textit{F.~Luca} and \textit{P.~Stănică} [J. Number Theory 102, No. 2, 298--305 (2003; Zbl 1049.11092)]. The proof depends on an interesting result concerning the joint distribution of several \(q\)-additive functions.
scientific article; zbMATH DE number 5149378