Category:Definitions/Carmichael Numbers

This category contains definitions related to Carmichael Numbers.
Related results can be found in Category:Carmichael Numbers.

An integer $n > 0$ is a Carmichael number if and only if:

$(1): \quad n$ is composite

$(2): \quad \forall a \in \Z: a \perp n: a^n \equiv a \pmod n$, or, equivalently, that $a^{n - 1} \equiv 1 \pmod n$.

That is, a Carmichael number is a composite number $n$ which satisfies $a^n \equiv a \pmod n$ for all integers $a$ which are coprime to it.