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Consider $\mathbb{Z}_{n}={}$ $\left\{\overline{0}, \overline{1},\dots,\overline{n-1} \right\}$, where $\overline{a}$ is residue class modulo $n$. Prove that for every $a\in \mathbb{Z}_n$ there exists $-a$ so that $a+(-a)=-a+a=0$.
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Tue, 01 Apr 2014 18:42 GMT