Question

Implications of Modular Arithmetic in the Complex Plane Defined as $z_1 \bmod z_2 = z_1 - z_2 \left\lfloor \frac{z_1}{z_2} \right\rfloor$?

score 101 · Answer 1 · 2021-10-31 03:24:36

101

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Implications of Modular Arithmetic in the Complex Plane Defined as $z_1 \bmod z_2 = z_1 - z_2 \left\lfloor \frac{z_1}{z_2} \right\rfloor$?

Published on 31 Oct 2021 - 3:24

score 469 · Answer 2 · 2021-11-04 22:41:22

469

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In calculating GCD in $\mathbb Z[i]$ does it matter if we switch $a$ and $b$?

Published on 04 Nov 2021 - 22:41

score 73 · Answer 3 · 2021-11-13 09:48:36

73

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What are the prime ideals in $\mathbb{Z}[i]$?

Published on 13 Nov 2021 - 9:48

score 983 · Answer 4 · 2021-11-14 05:03:15

983

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Prove that the Gaussian integers Z [i] form an integral domain

Published on 14 Nov 2021 - 5:03

score 33 · Answer 5 · 2021-11-14 22:42:28

33

Views

A question about Gaussian integers

Published on 14 Nov 2021 - 22:42

score 47 · Answer 6 · 2021-11-19 13:32:44

How do I find $a,b \in \mathbb{Z}$ s.t. $\{a c+b d+i(a d+b c) \mid c, d \in \mathbb{Z}\}$ consist of cmplx no. with real,imag part even or odd?

score 117 · Answer 7 · 2021-11-21 11:20:16

117

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How do I find $a,b\in\mathbb{Z}$ s.t. $\{ac-bd+i(ad+bc)\mid c, d\in\mathbb{Z}\}$ have real and imaginary parts both even or both odd?

Published on 21 Nov 2021 - 11:20

score 47 · Answer 8 · 2021-11-22 18:39:49

47

Views

Find the factorization of the following numbers in Z[i]. 11 + i ; 510 + 180i:

Published on 22 Nov 2021 - 18:39

score 159 · Answer 9 · 2021-11-27 20:17:47

159

Views

Proof that gaussian integers are an integral domain by contradiction.

Published on 27 Nov 2021 - 20:17

score 26 · Answer 10 · 2021-12-13 19:24:36

26

Views

Generator/generators for cyclic group $\mathbb Z[i]/(11-8i)$, given the following isomorphism:

Published on 13 Dec 2021 - 19:24

score 47 · Answer 11 · 2021-12-15 16:39:43

47

Views

If $p$ is a prime in $\mathbb{Z}$ and $(p)$ is a prime ideal in $\mathbb{Z}[i]$, then $x^2 \equiv -1\pmod{p}$ has no solution in $\mathbb{Z}[i]$

Published on 15 Dec 2021 - 16:39

score 50 · Answer 12 · 2021-12-30 02:57:16

50

Views

Gaussian numbers algorithmic operations.

Published on 30 Dec 2021 - 2:57

score 131 · Answer 13 · 2022-01-01 01:14:40

131

Views

The Diophantine equation $x^2\pm iy^2=z^3$ in Gaussian integers

Published on 01 Jan 2022 - 1:14

score 101 · Answer 14 · 2022-01-11 15:38:47

101

Views

Uniqueness of expansions of Gaussian integers to a Gaussian integer base

Published on 11 Jan 2022 - 15:38

score 151 · Answer 15 · 2022-01-12 22:30:23

151

Views

Homomorphism ring from integers to quotient ring of Gaussian integers

Published on 12 Jan 2022 - 22:30

List Question

Implications of Modular Arithmetic in the Complex Plane Defined as $z_1 \bmod z_2 = z_1 - z_2 \left\lfloor \frac{z_1}{z_2} \right\rfloor$?

In calculating GCD in $\mathbb Z[i]$ does it matter if we switch $a$ and $b$?

What are the prime ideals in $\mathbb{Z}[i]$?

Prove that the Gaussian integers Z [i] form an integral domain

A question about Gaussian integers

How do I find $a,b \in \mathbb{Z}$ s.t. $\{a c+b d+i(a d+b c) \mid c, d \in \mathbb{Z}\}$ consist of cmplx no. with real,imag part even or odd?

How do I find $a,b\in\mathbb{Z}$ s.t. $\{ac-bd+i(ad+bc)\mid c, d\in\mathbb{Z}\}$ have real and imaginary parts both even or both odd?

Find the factorization of the following numbers in Z[i]. 11 + i ; 510 + 180i:

Proof that gaussian integers are an integral domain by contradiction.

Generator/generators for cyclic group $\mathbb Z[i]/(11-8i)$, given the following isomorphism:

If $p$ is a prime in $\mathbb{Z}$ and $(p)$ is a prime ideal in $\mathbb{Z}[i]$, then $x^2 \equiv -1\pmod{p}$ has no solution in $\mathbb{Z}[i]$

Gaussian numbers algorithmic operations.

The Diophantine equation $x^2\pm iy^2=z^3$ in Gaussian integers

Uniqueness of expansions of Gaussian integers to a Gaussian integer base

Homomorphism ring from integers to quotient ring of Gaussian integers

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