Definition:Lucas-Carmichael Number/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$399$

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: $p^3 + 1 = \left({p + 1}\right) \left({p^2 - p + 1}\right)$.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $399$