Let $ n \geq 3 $. By factorising $ n $ or $n + 1 $ (as appropriate), show that $ \mathbb{Z}[\sqrt{-n}] $ is not a UFD
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
16559
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
150677
What are the integers $n$ such that $\mathbb{Z}[\sqrt{n}]$ is integrally closed?
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
114219
The map $f:\mathbb{Z}_3 \to \mathbb{Z}_6$ given by $f(x + 3\mathbb{Z}) = x + 6\mathbb{Z}$ is not well-defined
138944
Is $\mathbb Z[\sqrt{-3}]$ Euclidean under some other norm?
143069
What are the direct summands in $\mathbb{Z}^n$?
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
125604
Proof that $\mathbb{Z}$ has no zero divisors
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
50934
Let $x_n \in[0,1)$ s.t $x_n - \sqrt{n}\in \mathbb{Z}$. Prove that $X=\{x_n | n\in \mathbb{N}\}$ is dense in $[0,1]$.
153204
Euclidean domain $\mathbb{Z}[\sqrt{d}]$