Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3,6n+2, and 6n+1.
The smallest positive integer k = 5, so that: 6*1 + 5 =11, which is relatively prime to: 6*1 + 1=7, 6*1 + 2 =8 and 6*1 +3 =9. This is true for all n =1, 2, 3, 4........etc.
