Accessible Unlicensed Requires Authentication Published by De Gruyter November 5, 2010

On the Iteration of a Function Related to Euler's φ-Function

Joshua Harrington and Lenny Jones
From the journal


A unit x in a commutative ring R with identity is called exceptional if 1 − x is also a unit in R. For any integer n ≥ 2, define φe(n) to be the number of exceptional units in the ring of integers modulo n. Following work of Shapiro, Mills, Catlin and Noe on iterations of Euler's φ-function, we develop analogous results on iterations of the function φe, when restricted to a particular subset of the positive integers.

Received: 2009-02-23
Revised: 2010-03-29
Accepted: 2010-05-12
Published Online: 2010-11-05
Published in Print: 2010-November

© de Gruyter 2010