The distribution of relatively \(r\)-prime integers in residue classes
type: Item
instance of: scholarly article
title: The distribution of relatively \(r\)-prime integers in residue classes
zbMATH Open document ID: 0773.11054
author: J. E. Nymann
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: The natural numbers \(m_ 1,m_ 2,\dots,m_ k\) are called relatively \(r\)-prime, if no \(r\)-th power of an integer greater than 1 is a common divisor of all \(k\) numbers. An asymptotic representation is proved for the number of \(k\)-tuples of positive integers \((m_ 1,m_ 2,\dots,m_ k)\) for which \(1\leq m_ i\leq x\), \(m_ i\equiv a_ i\pmod h\), \(i=1,2,\dots,k\), and \(m_ 1,m_ 2,\dots,m_ k\) are relatively \(r\)- prime. The asymptotic formula is rather general and contains as special cases some known estimates for relatively prime integers and \(r\)-free numbers.
Mathematics Subject Classification ID: 11N25
zbMATH DE Number: 219347
zbMATH Keywords: relatively prime integers
zbMATH Keywords: \(k\)-free numbers
zbMATH Keywords: asymptotic formula
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072668
OpenAlex ID: W1992411385
DOI: 10.1216/RMJM/1181072668
description: scientific article; zbMATH DE number 219347