Some divisibility properties of the Euler function

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
3 Downloads (Pure)


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 languageEnglish
Pages (from-to)517-528
Number of pages12
JournalGlasgow Mathematical Journal
Issue number3
Publication statusPublished - Sep 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

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