show that all elements of the form $\pm(1 −\sqrt{2} )^n$ for $n \in \mathbb{Z}$ are distinct units
86807
The units of $\mathbb Z[\sqrt{2}]$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
83001
Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
108550
Elements of $\mathbb Q(2^{1/3})$
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
47186
$(1-\zeta_m)$ is a unit in $\mathbb{Z}[\zeta_m]$ if m contains at least two prime factors
158356
Need a proofreading why all the units are satisfied $a^2-2b^2 =\pm1$ for $\mathbf{Z}[\sqrt{2}]$
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
35222
Characterizing units in polynomial rings
122312
How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
102971
Product of all elements of a finite group with an unique element of order 2
20438
Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
113474
An $n \times n$ matrix $M$ of integers has the property that $M_{ab} = M_{xy}$ iff $a+b=x+y$. How many distinct elements are there in $M$?