Korselt's Theorem

Theorem
Let $n > 0$ be an odd integer.

Then $n$ is a Carmichael number  both of the following conditions hold for every prime factor $p$ of $n$:
 * $(1): \quad p^2 \nmid n$
 * $(2): \quad \left({p - 1}\right) \mathrel \backslash \left({n - 1}\right)$

Also known as
Korselt's theorem is also seen referred to as Korselt's criterion.