\begin{definition}[Definition:Lucas-Carmichael Number]
Let $n \in \Z_{>0}$ be a positive composite number which is odd and square-free.
Let $n$ have the property that:
:$p \divides n \implies \paren {p + 1} \divides \paren {n + 1}$
where:
:$p$ is prime
:$p \divides n$ denotes that $p$ is a divisor of $n$.
Then $n$ is classified as a '''Lucas-Carmichael number'''.
\end{definition}