The Arithmetic of Carmichael Quotients

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.