On two functions arising in the study of the Euler and Carmichael quotients

Florian Luca; Min Sha; Igor E. Shparlinski

doi:10.4064/cm6910-3-2017

On two functions arising in the study of the Euler and Carmichael quotients

Florian Luca, Min Sha, Igor E. Shparlinski

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

1 Citation (Scopus)

Abstract

We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.

Original language	English
Pages (from-to)	179-192
Number of pages	14
Journal	Colloquium Mathematicum
Volume	149
Issue number	2
DOIs	https://doi.org/10.4064/cm6910-3-2017
Publication status	Published - 2017
Externally published	Yes

Keywords

Carmichael function
Carmichael quotient
Euler function
Euler quotient
greatest common divisor

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10.4064/cm6910-3-2017

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abstract = "We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.",

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AU - Luca, Florian

AU - Sha, Min

AU - Shparlinski, Igor E.

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KW - Carmichael function

KW - Carmichael quotient

KW - Euler function

KW - Euler quotient

KW - greatest common divisor

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On two functions arising in the study of the Euler and Carmichael quotients

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Keywords

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