Euler's function in residue classes
type: Item
instance of: scholarly article
title: Euler's function in residue classes
zbMATH Open document ID: 0919.11006
DOI: 10.1023/A:1009753405498
published in: The Ramanujan Journal
publication date: 1999-09-01T00:00:00Z
review text: The authors discuss the question if there are infinitely many values of Euler's function \(\varphi\) in a given residue class \(r\bmod m\). It is clear that this is not the case for a class not containing even numbers. In the paper under review it is proved that a residue class containing a multiple of 4 has this property. The authors point out that 4 cannot be replaced by 2. This is shown by \textit{K. Ford}, \textit{S. Konyagin} and \textit{C. Pomerance} [Number theory in progress, Zakopane, Poland 1997, Vol. 2, 805-812 (1999)]. Further the authors derive asymptotic formulas for the distribution of \(\varphi(n)\) in the residue classes mod 12.
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11N69
Mathematics Subject Classification ID: 11B50
zbMATH DE Number: 1203254
zbMATH Keywords: distribution in residue classes
zbMATH Keywords: values of Euler's function
zbMATH Keywords: asymptotic formulas
author: Thomas P. Dence
author: Carl Pomerance
reviewed by: Thomas Maxsein
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1203254