What the least common multiple divides
type: Item
instance of: scholarly article
title: What the least common multiple divides
zbMATH Open document ID: 0810.11001
author: Gerald Myerson
published in: Journal of Number Theory
publication date: 1995-04-11T00:00:00Z
review text: Let \(a_ 1, a_ 2,\dots\) be a sequence satisfying \((a_ m, a_ n)= a_{(m,n)}\) for all \(m\), \(n\), where \((\cdot, \cdot)\) stands for the greatest common divisor. Let \(L(n)\) be the l.c.m., and \(P(n)\) the product of the first \(n\) terms of the sequence. The main result of the paper is that \(L(n)\) divides the quotient of \(P(n)\) by \(P(n/2) P(n/3) P(n/7) P(n/43)\dots\), where each term in the sequence \(2,3,7,43,\dots\) is one greater than the product of all the preceding terms. The extent to which this result is best possible is also discussed in the paper.
reviewed by: Štefan Porubský
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11N80
zbMATH DE Number: 638547
zbMATH Keywords: least common multiple
zbMATH Keywords: multinomial coefficient
MaRDI profile type: Publication
full work available at URL: jnth.1994.1054
OpenAlex ID: W4213219376
DOI: 10.1006/JNTH.1994.1054
description: scientific article; zbMATH DE number 638547