Let $n=(6t+1)(12t+1)(18t+1)$. Show that $a^{n-1} \equiv 1\pmod n$ if $(a,n)=1$
Suppose k is an integer such that $6k + 1$, $12k + 1$, $18k + 1$ are primes. Show that $n = (6k + 1)(12k + 1)(18k + 1)$ is a Carmichael number.