Show that $$k(\mathbb{Z}/n\mathbb{Z})\cong (\gcd(n,k)\mathbb{Z})/n\mathbb{Z}.$$
I want to see as many as possible proofs of this nice fact.
2026-04-03 09:08:14.1775207294
A nice group isomorphism
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We have $k\mathbb{Z}+n\mathbb{Z}=\gcd(n,k)\mathbb{Z}$, by the Euclidean algorithm, and taking the quotient by $n\mathbb{Z}$ gives the result.