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AAA is a non-empty proper subset of Z\mathbb ZZ with at least two elements, and with the following property:
If aaa and bbb are distinct elements of A,A,A, then −a,-a,−a, a+2b,a+2b,a+2b, and a+19a+19a+19 are also elements of A.A.A.
Find mina∈Aa≠0(∣a∣).\min \limits_{a \in A \atop a \neq 0}\big(|a|\big).a=0a∈Amin(∣a∣).
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