The arithmetic of Carmichael quotients

Min Sha

doi:10.1007/s10998-014-0079-3

The arithmetic of Carmichael quotients

Min Sha^*

^*Corresponding author for this work

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

11 Citations (Scopus)

Abstract

Carmichael quotients for an integer ≥ 2 are introduced analogous to Fermat quotients, by using Carmichael function λ(m). Various properties of these new quotients are investigated, such as basic arithmetic properties, sequences derived from Carmichael quotients, Carmichael-Wieferich numbers, and so on. Finally, we link Carmichael quotients to perfect nonlinear functions.

Original language	English
Pages (from-to)	11-23
Number of pages	13
Journal	Periodica Mathematica Hungarica
Volume	71
Issue number	1
DOIs	https://doi.org/10.1007/s10998-014-0079-3 https://doi.org/10.1007/s10998-017-0227-7
Publication status	Published - Sept 2015
Externally published	Yes

Bibliographical note

A correction to this record can be found in Period Math Hung (2018) 76:271–273, https://doi.org/10.1007/s10998-017-0227-7

Keywords

Carmichael function
Carmichael quotient
Carmichael-Wieferich number
Perfect nonlinear function

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AB - Carmichael quotients for an integer ≥ 2 are introduced analogous to Fermat quotients, by using Carmichael function λ(m). Various properties of these new quotients are investigated, such as basic arithmetic properties, sequences derived from Carmichael quotients, Carmichael-Wieferich numbers, and so on. Finally, we link Carmichael quotients to perfect nonlinear functions.

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KW - Carmichael-Wieferich number

KW - Perfect nonlinear function

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The arithmetic of Carmichael quotients

Abstract

Bibliographical note

Keywords

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