Definition:Lucas-Carmichael Number

Definition
Let $n \in \Z_{>0}$ be a positive composite number which is odd and square-free. Let $n$ have the property that:
 * $p \mathrel \backslash n \implies \left({p + 1}\right) \mathrel \backslash \left({n + 1}\right)$

where:
 * $p$ is prime
 * $p \mathrel \backslash n$ denotes that $p$ is a divisor of $n$.

Then $n$ is classified as a Lucas-Carmichael number.