On the Iteration of a Function Related to Euler’s Φ-function

Abstract

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.

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Cite this paper

@inproceedings{Harrington2010OnTI, title={On the Iteration of a Function Related to Euler’s Φ-function}, author={Joshua Harrington and Lenny Jones}, year={2010} }