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I have been learning about quotient rings, and have come across the following ring: $ (\mathbb Z/n \mathbb Z)$, the ring of residue classes mod $n$.

I have found that the set of units in $ (\mathbb Z/n \mathbb Z)$ is $$ (\mathbb Z/n \mathbb Z) ^X = \{k+n \mathbb Z : gcd(n,k)=1\} $$

How can I see that this is true?

mathreads
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1 Answers1

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One inclusion is straightforward. The other follows from the existence of the extended Euclidean algorithm.

tomasz
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