The Arithmetic of Carmichael Quotients

Abstract

Carmichael quotients for an integer $m\ge 2$ are introduced analogous to Fermat quotients, by using Carmichael function $\lambda (m)$. 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.

Proposition 4.3 is corrected

References in corpus (1)

• Fermat quotients: Exponential sums, value set and primitive roots

Cited by in corpus (4)

• Trace representation and linear complexity of binary sequences derived from Fermat quotients
• On the $k$-error linear complexity of binary sequences derived from polynomial quotients
• Trace representation of pseudorandom binary sequences derived from Euler quotients
• Polynomial quotients: Interpolation, value sets and Waring's problem