Brian Bi
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Section 2.3. Subgroups of the Additive Group of Integers

Exercise 2.3.3(a) Let \(S\) be a nonempty, possibly infinite set of integers. If \(S = \{0\}\), then define the GCD to be 0. Otherwise, the subgroup of \(\mathbb{Z}^+\) generated by \(S\) contains a least positive element \(d\) and by Theorem 2.3.3, this subgroup is precisely \(d\mathbb{Z}\). We define the GCD of \(S\) to be \(d\).