Regularity of patterns in the factorization of n!
type: Item
instance of: scholarly article
title: Regularity of patterns in the factorization of n!
zbMATH Open document ID: 1124.11036
author: Daniel Berend
author: G. A. Kolesnik
published in: Journal of Number Theory
publication date: 2007-05-04T00:00:00Z
review text: 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.
reviewed by: Robert F. Tichy
Mathematics Subject Classification ID: 11K31
Mathematics Subject Classification ID: 11K36
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 5149378
zbMATH Keywords: uniform distribution
zbMATH Keywords: joint distribution
zbMATH Keywords: factorials
MaRDI profile type: Publication
full work available at URL: j.jnt.2006.08.010
OpenAlex ID: W1974262641
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DOI: 10.1016/J.JNT.2006.08.010
description: scientific article; zbMATH DE number 5149378