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

2017/04/30 by Luca, Florian, Sha, Min, Shparlinski, Igor E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1705.00388

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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• The Arithmetic of Carmichael Quotients
• The Asymptotic Behavior of Compositions of the Euler and Carmichael Functions
• Euler-type Recurrence Relation for Arbitrary Arithmetical Function
• Euler pseudoprimes for half of the bases
• Arithmetic Functions and Geometry