Question

Any Gaussian prime dividing a product of gaussian primes is equal to one of those gaussian primes

score 354 · Answer 1 · 2021-02-18 23:00:36

354

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Any Gaussian prime dividing a product of gaussian primes is equal to one of those gaussian primes

Published on 18 Feb 2021 - 23:00

score 522 · Answer 2 · 2021-02-21 04:20:23

522

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$1+i$ is a prime element of ring of Gaussian integers.

Published on 21 Feb 2021 - 4:20

score 27 · Answer 3 · 2021-02-26 06:02:47

27

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prove that $\forall k\geqslant1\land k\in\mathbb{Z}.\nexists q\in\mathbb{Z}.q^{2}=(k-i)(k+i)$

Published on 26 Feb 2021 - 6:02

score 56 · Answer 4 · 2021-02-26 11:07:43

56

Views

prove or disprove in $\mathbb{Z}[i]$ decomposition of real integer to 2 elements with the same norm is unique up to multiplying by unit

Published on 26 Feb 2021 - 11:07

score 75 · Answer 5 · 2021-03-01 17:05:51

75

Views

Irreducible gaussian integers with prime norm in $\mathbb{Z}$

Published on 01 Mar 2021 - 17:05

score 79 · Answer 6 · 2021-03-07 03:32:41

79

Views

are there infinitely many primes $p,q$ such that $pq=a^2+b^4$

Published on 07 Mar 2021 - 3:32

score 713 · Answer 7 · 2021-03-12 09:42:57

713

Views

ideals of ring of Gaussian integers modulo $n$

Published on 12 Mar 2021 - 9:42

score 103 · Answer 8 · 2021-03-24 05:00:52

103

Views

Number of distinct associated classes of the ring $\mathbb{Z}_n[i]$.

Published on 24 Mar 2021 - 5:00

score 36 · Answer 9 · 2021-03-27 12:43:46

36

Views

Example Gaussian Primes

Published on 27 Mar 2021 - 12:43

score 88 · Answer 10 · 2021-04-01 05:42:42

88

Views

(Proof explanation) $\mathbb{Z} /\left(a^{2}+b^{2}\right) \mathbb{Z} \cong \mathbb{Z}[i] /\langle a+b i\rangle$ doesn't hold

Published on 01 Apr 2021 - 5:42

score 81 · Answer 11 · 2021-04-07 12:50:50

81

Views

Counting number of prime factorizations

Published on 07 Apr 2021 - 12:50

score 33 · Answer 12 · 2021-04-12 22:33:39

33

Views

Trivial Factor of Gaussian Primes

Published on 12 Apr 2021 - 22:33

score 52 · Answer 13 · 2026-03-25 09:29:57

52

Views

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Published on 25 Mar 2026 - 9:29

score 426 · Answer 14 · 2021-04-25 17:07:54

426

Views

Fermat's Last Theorem ($n=4$) using the Gaussian integers

Published on 25 Apr 2021 - 17:07

score 379 · Answer 15 · 2026-02-23 15:29:58

379

Views

Can you explain this relation between finite fields and circles?

Published on 23 Feb 2026 - 15:29

List Question

Any Gaussian prime dividing a product of gaussian primes is equal to one of those gaussian primes

$1+i$ is a prime element of ring of Gaussian integers.

prove that $\forall k\geqslant1\land k\in\mathbb{Z}.\nexists q\in\mathbb{Z}.q^{2}=(k-i)(k+i)$

prove or disprove in $\mathbb{Z}[i]$ decomposition of real integer to 2 elements with the same norm is unique up to multiplying by unit

Irreducible gaussian integers with prime norm in $\mathbb{Z}$

are there infinitely many primes $p,q$ such that $pq=a^2+b^4$

ideals of ring of Gaussian integers modulo $n$

Number of distinct associated classes of the ring $\mathbb{Z}_n[i]$.

Example Gaussian Primes

(Proof explanation) $\mathbb{Z} /\left(a^{2}+b^{2}\right) \mathbb{Z} \cong \mathbb{Z}[i] /\langle a+b i\rangle$ doesn't hold

Counting number of prime factorizations

Trivial Factor of Gaussian Primes

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Fermat's Last Theorem ($n=4$) using the Gaussian integers

Can you explain this relation between finite fields and circles?

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