Question

Over Gaussian integers, can every prime be $p \equiv 1 \text{ mod }4$ be expressed as $(a + bi)(a - bi)$ in almost unique manner?

score 920 · Answer 1 · 2016-04-11 00:01:02

920

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Over Gaussian integers, can every prime be $p \equiv 1 \text{ mod }4$ be expressed as $(a + bi)(a - bi)$ in almost unique manner?

Published on 11 Apr 2016 - 0:01

score 48 · Answer 2 · 2016-05-09 22:52:04

48

Views

A counterexample to a statement

Published on 09 May 2016 - 22:52

score 129 · Answer 3 · 2016-05-31 16:50:20

129

Views

What is the involvement of the Gaussian primes in a positive integer being expressed as the sum of two squares?

Published on 31 May 2016 - 16:50

score 470 · Answer 4 · 2013-05-07 04:07:05

470

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Congruence Classes in the Guassian Integers?

Published on 07 May 2013 - 4:07

score 714 · Answer 5 · 2026-03-25 03:29:06

714

Views

Pythagorean Primes

Published on 25 Mar 2026 - 3:29

score 32.7k · Answer 6 · 2013-12-09 21:01:54

32.7k

Views

Prove that the Gaussian Integer's ring is a Euclidean domain

Published on 09 Dec 2013 - 21:01

score 205 · Answer 7 · 2017-04-10 01:57:04

205

Views

How to generate similar identities to $(5+i)^4=2(1+i)(239+i)$

Published on 10 Apr 2017 - 1:57

score 574 · Answer 8 · 2017-04-13 19:38:03

574

Views

The Gaussian Integers, $\Bbb Z[i]$, is isomorphic to what familiar group?

Published on 13 Apr 2017 - 19:38

score 88 · Answer 9 · 2017-04-24 15:55:00

88

Views

Proving that the ring $\mathbb Z[i]/\langle{p}\rangle$ is a field with $p^2$ elements.

Published on 24 Apr 2017 - 15:55

score 52 · Answer 10 · 2017-04-26 22:40:36

52

Views

Find all primes $x$ in a Euclidean domain $ Z[i]$ for which $|x|^2 \leq 16$.

Published on 26 Apr 2017 - 22:40

score 1k · Answer 11 · 2017-05-10 17:29:34

1k

Views

How does Euclidean Domain imply Unique Factorization domain for Gaussian Integers?

Published on 10 May 2017 - 17:29

score 535 · Answer 12 · 2017-05-11 03:13:41

535

Views

How Gaussian Quadreture deals with improper integral.

Published on 11 May 2017 - 3:13

score 54 · Answer 13 · 2017-05-22 17:59:31

54

Views

Gaussian integers: Proof that if $N(\alpha) = N(\beta)$ then $\alpha = t \beta, t \in \{1, -1, i, -i \}$

Published on 22 May 2017 - 17:59

score 4.2k · Answer 14 · 2017-06-04 17:51:34

4.2k

Views

The quotient ring $\mathbb{Z}[i]/(1 + i)$

Published on 04 Jun 2017 - 17:51

score 178 · Answer 15 · 2017-07-03 02:14:48

178

Views

How do you prove this involving Gaussian integers?

Published on 03 Jul 2017 - 2:14

List Question

Over Gaussian integers, can every prime be $p \equiv 1 \text{ mod }4$ be expressed as $(a + bi)(a - bi)$ in almost unique manner?

A counterexample to a statement

What is the involvement of the Gaussian primes in a positive integer being expressed as the sum of two squares?

Congruence Classes in the Guassian Integers?

Pythagorean Primes

Prove that the Gaussian Integer's ring is a Euclidean domain

How to generate similar identities to $(5+i)^4=2(1+i)(239+i)$

The Gaussian Integers, $\Bbb Z[i]$, is isomorphic to what familiar group?

Proving that the ring $\mathbb Z[i]/\langle{p}\rangle$ is a field with $p^2$ elements.

Find all primes $x$ in a Euclidean domain $ Z[i]$ for which $|x|^2 \leq 16$.

How does Euclidean Domain imply Unique Factorization domain for Gaussian Integers?

How Gaussian Quadreture deals with improper integral.

Gaussian integers: Proof that if $N(\alpha) = N(\beta)$ then $\alpha = t \beta, t \in \{1, -1, i, -i \}$

The quotient ring $\mathbb{Z}[i]/(1 + i)$

How do you prove this involving Gaussian integers?

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