$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
6121
Quotient ring of Gaussian integers
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
119702
Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
57434
$SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$
50241
Cardinality of the quotient ring $\mathbb Z_5[i]/\langle 1+i\rangle$
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
69582
Is it true that: $a+bi$ is prime in $\mathbb{Z}[i]$ if and only if $a^2+b^2$ is prime in $\mathbb{Z}$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
102721
Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
61987
$x^2+1=0$ in $\mathbb{Z}_7$
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.