Some divisibility properties of the Euler function

William D. Banks; Florian Luca; Igor E. Shparlinski

doi:10.1017/S0017089505002752

Some divisibility properties of the Euler function

William D. Banks^*, Florian Luca, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

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Abstract

Let $\varphi(\cdot)$ denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as aⁿ ≡ 1 (mod φ(n)), and we estimate the number of positive integers $n\le x$ satisfying these conditions.

Original language	English
Pages (from-to)	517-528
Number of pages	12
Journal	Glasgow Mathematical Journal
Volume	47
Issue number	3
DOIs	https://doi.org/10.1017/S0017089505002752
Publication status	Published - Sept 2005

Bibliographical note

Copyright 2005 Cambridge University Press. Article originally published in Glasgow Mathematical Journal, Vol. 47, Issue 3, pp. 517-528. The original article can be found at http://dx.doi.org/10.1017/S0017089505002752.

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Some divisibility properties of the Euler function

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