Question

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

score 245 · Answer 1 · 2026-03-19 17:50:16

245

Views

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

Published on 19 Mar 2026 - 17:50

score 448 · Answer 2 · 2026-03-20 11:06:03

448

Views

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

Published on 20 Mar 2026 - 11:06

score 176 · Answer 3 · 2026-03-20 05:05:37

176

Views

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

Published on 20 Mar 2026 - 5:05

score 1.2k · Answer 4 · 2026-03-20 03:55:07

1.2k

Views

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

Published on 20 Mar 2026 - 3:55

score 64 · Answer 5 · 2026-03-22 05:41:19

64

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 22 Mar 2026 - 5:41

score 7.6k · Answer 6 · 2026-03-20 05:58:46

7.6k

Views

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

Published on 20 Mar 2026 - 5:58

score 145 · Answer 7 · 2026-03-20 06:18:35

145

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 20 Mar 2026 - 6:18

score 522 · Answer 8 · 2026-03-19 18:20:56

522

Views

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

Published on 19 Mar 2026 - 18:20

score 842 · Answer 9 · 2026-03-20 11:01:51

842

Views

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

Published on 20 Mar 2026 - 11:01

score 316 · Answer 10 · 2026-03-20 05:28:57

316

Views

Solve Equations in the ring of Gaussian Integers

Published on 20 Mar 2026 - 5:28

score 667 · Answer 11 · 2026-03-20 05:24:36

667

Views

Ring of Gaussian integers modulo p=4n+3

Published on 20 Mar 2026 - 5:24

score 83 · Answer 12 · 2026-03-25 01:17:02

83

Views

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

Published on 25 Mar 2026 - 1:17

score 270 · Answer 13 · 2026-03-25 01:15:01

270

Views

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

Published on 25 Mar 2026 - 1:15

score 103 · Answer 14 · 2026-03-25 01:21:53

103

Views

number theory problem, about arctan and pi

Published on 25 Mar 2026 - 1:21

score 579 · Answer 15 · 2026-03-25 01:18:51

579

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 25 Mar 2026 - 1:18

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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