location:  Publications → journals → CMB
Abstract view

# The Distribution of Totatives

Published:2002-03-01
Printed: Mar 2002
• R. R. Hall
• P. Shiu
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

D.~H.~Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a given integer. This led to various problems considered by P.~Erd\H os, who made a conjecture on such distributions. We prove his conjecture by establishing a theorem on the ordering of residues.
 Keywords: Euler's function, totatives
 MSC Classifications: 11A05 - Multiplicative structure; Euclidean algorithm; greatest common divisors 11A07 - Congruences; primitive roots; residue systems 11A25 - Arithmetic functions; related numbers; inversion formulas