Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.
120699
Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
119702
Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
49061
Show that $\int_{\partial P}z\frac {f'(z)} {f(z)} dz $ is on the lattice $\Lambda$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
76292
Showing that $f$ is identically $0$ on $\mathbb{D}$
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
55742
Showing that $f_{2n+1}=f_{n+1}^2+f_n^2$.
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.