Chapter 4.4, Problem 49E

Use Exercise 48 to show that every integer of the form $\left(\text{6}m+\text{1}\right)\left(\text{12}m+\text{1}\right)\left(\text{18}m+\text{1}\right)$ , where m is a positive integer and $\text{6}m+\text{1},\text{ 12}m+\text{1}$ , and $\text{18}m+\text{1}$

1. are all primes, is a Carmichael number
2. Use part(a) to show that 172,947,529 is a Carmichael number.