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I need to find all the values of $a$ and $n$ that gives $\{0,a\}$ is a subgroup of the group $(\mathbb{Z}_n,+)$. Assum $n \geq 2$ and $a \neq 0$.

Actually I thing that for each $a$ and $n$ we will get that this is a subgroup ($0$ identity element) Am I wrong??

1 Answers 1

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$\{0,1\}$ is not a subgroup of $\mathbb{Z}_n$ for $n \geq 3$.

Hint: Notice that $\{0,a\}$ is a subgroup of $\mathbb{Z}_n$ iff $2a=0$.

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    I was given that a is not zero so...Thank you very much for your help2012-12-29