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.
