Euler's equation \(\phi (x)=k\) with no solution
type: Item
instance of: scholarly article
title: Euler's equation \(\phi (x)=k\) with no solution
zbMATH Open document ID: 0668.10004
DOI: 10.1016/0022-314X(89)90029-2
author: Konstantine Spyropoulos
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \(\phi\) denote the Euler totient function. The author finds two classes of values of k for which the equation \(\phi (x)=k\) has no solution in x. In both classes k is of the form \(2^ n p_ 1^{a(1)}... p_ m^{a(m)},\) where n, a(1),...,a(m) are positive integers and \(p_ 1,...,p_ m\) distinct odd primes satisfying certain conditions. The proofs are elementary.
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 4093542
zbMATH Keywords: Euler's phi-function
zbMATH Keywords: Euler's equation
zbMATH Keywords: Dirichlet's theorem
reviewed by: Pentti Haukkanen
MaRDI profile type: Publication
cites work: The Equation Φ(x) = k
cites work: Sur l'équation \(\varphi (x) = m\)
description: scientific article; zbMATH DE number 4093542