The arithmetic of Carmichael quotients

Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Citations (Scopus)


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 languageEnglish
Pages (from-to)11-23
Number of pages13
JournalPeriodica Mathematica Hungarica
Issue number1
Publication statusPublished - Sep 2015
Externally publishedYes

Bibliographical note

A correction to this record can be found in Period Math Hung (2018) 76:271–273,


  • Carmichael function
  • Carmichael quotient
  • Carmichael-Wieferich number
  • Perfect nonlinear function

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