Definition:Lucas-Carmichael Number/Mistake

Source Work

 * The Dictionary
 * $399$
 * $399$

Mistake

 * The smallest Lucas-Carmichael number $n$, such that if $p$ divides $n$, then $p + 1$ divides $n + 1$.

It also needs to be stated that:
 * $n$ is composite, otherwise all primes would trivially be Lucas-Carmichael numbers


 * $n$ is odd and square-free, in order to eliminate several other classes of integer for example, cubes of primes: $p^3 + 1 = \left({p + 1}\right) \left({p^2 - p + 1}\right)$.