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Let n greater than or equal to 2 and let k1,...,kn be positive integers. Recall that...

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Advance Math

Let n greater than or equal to 2 and let k1,...,kn bepositive integers. Recall that Ck1,..., Ckn denote the cyclicgroups of order k1,...,kn. Prove by induction that their directproduct Ck1×Ck2×....×Ckn is cyclic if and only if the ki's arepairwise coprime which means gcd(ki,kj)=1 for every i not equals jin {1,...n}.

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