Suppose that k is chosen so that the three numbers 6k+1, 12k+1, 18k+1

  

Suppose that k is chosen so that the three numbers 6k+1, 12k+1, 18k+1 are all prime numbers.
a) Prove that their product n= (6k+1)(12k+1)(18k+1) is a Carmichael number.
b) Find the five first values of k for which this method works and give the Carmichael number produced by the method