Abstract Algebra: Theory and Applications · Problem 9.4.53

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-subgroups-gcd

Problem

Let m,n∈Zm, n \in \mathbb{Z}. Prove that ⟨m,n⟩=⟨d⟩\langle m, n \rangle = \langle d \rangle if and only if d=gcd⁡(m,n)d = \gcd(m, n).

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