\begin{definition}[Definition:Carmichael Number]
An integer $n > 0$ is a '''Carmichael number''' {{iff}}:
: $(1): \quad n$ 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.
\end{definition}