The Arithmetic of Carmichael Quotients

Details The Arithmetic of Carmichael Quotients The Arithmetic of Carmichael Quotients

2011-08-12

arxiv.org/abs/1108.2579v3

Mathematics

Number Theory

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Scientific paper

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, Carmichael-Wieferich numbers, non-vanishing, equidistribution, sequences derived from Carmichael quotients and so on. At last, we link Carmichael quotients to the discrete logarithm problem.

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