If $R=\mathbb{Z}[\sqrt{p}]$ with $p$ an odd prime and $I=(2,1+\sqrt{p})$, then $I^2=(2)$
126429
Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$.
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
104917
Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
42875
The prime elements of the ring $ \mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right] $.
6453
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
34588
Number Theory: $p!+p=n^2$, $p$ = prime
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
2771
A group has odd number of elements iff each element is a square, $a=b^2$.
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
23048
The ring $\mathbb Z[\sqrt{-2}]= \{a+b\sqrt{-2} ; a\in \mathbb Z,b\in \mathbb Z \}$ has a Euclidean algorithm
80304
Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers