Question

$Z[i]/(2+3i) \simeq Z/13Z$ is my proof correct?

score 256 · Answer 1 · 2026-05-05 10:45:52

256

Views

$Z[i]/(2+3i) \simeq Z/13Z$ is my proof correct?

Published on 05 May 2026 - 10:45

score 454 · Answer 2 · 2026-05-05 04:10:31

454

Views

Deducing whether elements are prime in $\mathbb{Z}[\sqrt{-2}]$

Published on 05 May 2026 - 4:10

score 183 · Answer 3 · 2026-05-03 08:50:09

183

Views

Are there any interesting results in quadratic extensions that adjoin $2^k$th roots of unity beyond the Gaussian Integers?

Published on 03 May 2026 - 8:50

score 1.2k · Answer 4 · 2026-05-05 02:05:08

1.2k

Views

Solve in $\mathbb{Z}$ the equation $x^4 + 1 = 2y^2$.

Published on 05 May 2026 - 2:05

score 72 · Answer 5 · 2026-05-05 06:21:18

72

Views

If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Published on 05 May 2026 - 6:21

score 7.6k · Answer 6 · 2026-05-03 00:27:17

7.6k

Views

Prove that $\mathbb{Z}[i]$ is an integral domain.

Published on 03 May 2026 - 0:27

score 152 · Answer 7 · 2026-05-05 04:16:34

152

Views

Let $α=a+bi \in\mathbb{Z}[i]$ with $\gcd(a, b)=1$. Show that there exists $c\in\mathbb{Z}$ such that $c+i$ is a multiple of $α$ in $\mathbb{Z}[i]$.

Published on 05 May 2026 - 4:16

score 528 · Answer 8 · 2026-05-07 13:42:17

528

Views

Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

Published on 07 May 2026 - 13:42

score 846 · Answer 9 · 2026-05-04 10:33:37

846

Views

If $ p \equiv 3 (\bmod{4}) $ is a rational prime, then p is a Gaussian prime

Published on 04 May 2026 - 10:33

score 321 · Answer 10 · 2026-05-01 05:41:18

321

Views

Solve Equations in the ring of Gaussian Integers

Published on 01 May 2026 - 5:41

score 671 · Answer 11 · 2026-04-18 07:26:49

671

Views

Ring of Gaussian integers modulo p=4n+3

Published on 18 Apr 2026 - 7:26

score 86 · Answer 12 · 2026-04-29 12:56:39

86

Views

When does a $n \in \mathbb{Z}$ can be written as $n=A^2+B^2$?

Published on 29 Apr 2026 - 12:56

score 273 · Answer 13 · 2026-04-29 12:56:37

273

Views

Nonunit element in $\mathbb{Z}[i]$

Published on 29 Apr 2026 - 12:56

score 106 · Answer 14 · 2026-04-29 12:56:50

106

Views

number theory problem, about arctan and pi

Published on 29 Apr 2026 - 12:56

score 581 · Answer 15 · 2026-04-18 08:30:11

581

Views

Let $\alpha \in \mathbb Z [\sqrt{-1}]$. Is it true that $\mathbb Z[\alpha]/I$ is finite for any non-zero ideal $I$ of $\mathbb Z[\alpha]$?

Published on 18 Apr 2026 - 8:30

List Question

$Z[i]/(2+3i) \simeq Z/13Z$ is my proof correct?

Deducing whether elements are prime in $\mathbb{Z}[\sqrt{-2}]$

Are there any interesting results in quadratic extensions that adjoin $2^k$th roots of unity beyond the Gaussian Integers?

Solve in $\mathbb{Z}$ the equation $x^4 + 1 = 2y^2$.

If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Prove that $\mathbb{Z}[i]$ is an integral domain.

Let $α=a+bi \in\mathbb{Z}[i]$ with $\gcd(a, b)=1$. Show that there exists $c\in\mathbb{Z}$ such that $c+i$ is a multiple of $α$ in $\mathbb{Z}[i]$.

Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

If $ p \equiv 3 (\bmod{4}) $ is a rational prime, then p is a Gaussian prime

Solve Equations in the ring of Gaussian Integers

Ring of Gaussian integers modulo p=4n+3

When does a $n \in \mathbb{Z}$ can be written as $n=A^2+B^2$?

Nonunit element in $\mathbb{Z}[i]$

number theory problem, about arctan and pi

Let $\alpha \in \mathbb Z [\sqrt{-1}]$. Is it true that $\mathbb Z[\alpha]/I$ is finite for any non-zero ideal $I$ of $\mathbb Z[\alpha]$?

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