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:
 * $p \divides n \implies \paren {p + 1} \divides \paren {n + 1}$

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

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