Let n greater than or equal to 2 and let k1,...,kn be
positive integers. Recall that Ck1,..., Ckn denote the cyclic
groups of order k1,...,kn. Prove by induction that their direct
product Ck1×Ck2×....×Ckn is cyclic if and only if the ki's are
pairwise coprime which means gcd(ki,kj)=1 for every i not equals j
in {1,...n}.