Question

For Eisenstein numbers $a + b\frac{1+\sqrt{3} i}{2}$ with $0 \le a, b \le n$ how can I efficiently identify all of the primes?

score 152 · Answer 1 · 2023-04-29 01:25:52

152

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For Eisenstein numbers $a + b\frac{1+\sqrt{3} i}{2}$ with $0 \le a, b \le n$ how can I efficiently identify all of the primes?

Published on 29 Apr 2023 - 1:25

score 110 · Answer 2 · 2026-03-27 15:47:33

110

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Eisenstein Integers modulo $(1-\omega)^2$

Published on 27 Mar 2026 - 15:47

score 77 · Answer 3 · 2023-09-23 15:59:08

77

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$\exists X, Y, Z \in \mathbb{Z}[\omega]$ such that $X^3 + Y^3 + Z^3 = \omega$?

Published on 23 Sep 2023 - 15:59

score 58 · Answer 4 · 2026-03-30 04:57:55

58

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Automorphism groups of $\mathbf Z$, $\mathbf Z[i]$, $\mathbf Z[\omega]$

Published on 30 Mar 2026 - 4:57

score 34 · Answer 5 · 2026-04-20 04:17:26

34

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Let $\pi \in \mathbb{Z}[\omega]$ be a prime. Then $\frac{\mathbb{Z}[\omega]}{\pi \mathbb{Z}[\omega]}$ has $N(\pi)$ elements

Published on 20 Apr 2026 - 4:17

score 96 · Answer 6 · 2026-05-05 08:35:23

96

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Eisenstein integers with norm value of 5

Published on 05 May 2026 - 8:35

score 92 · Answer 7 · 2026-05-10 12:51:05

92

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Cubic non-residue calculation

Published on 10 May 2026 - 12:51

score 20 · Answer 8 · 2026-04-06 16:20:26

20

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Law of cubic reciprocity for a primary prime of norm 3

Published on 06 Apr 2026 - 16:20

score 238 · Answer 9 · 2026-05-07 16:41:16

238

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Eisenstein Integers

Published on 07 May 2026 - 16:41

score 522 · Answer 10 · 2026-04-22 17:45:32

522

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Natural generalizations of Gaussian & Eisenstein integers?

Published on 22 Apr 2026 - 17:45

score 2k · Answer 11 · 2026-03-09 03:46:21

2k

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On proving that $\mathbb{Z}[\omega]$ is a Euclidean domain.

Published on 09 Mar 2026 - 3:46

score 617 · Answer 12 · 2026-04-10 10:00:33

617

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Understanding a congruence relation in $\mathbb{Z}[\omega]$

Published on 10 Apr 2026 - 10:00

score 3.6k · Answer 13 · 2026-04-16 09:49:13

3.6k

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Primes congruent to 1 mod 6

Published on 16 Apr 2026 - 9:49

score 207 · Answer 14 · 2020-07-31 21:01:34

207

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How to find all solutions for : $a^3 \equiv b^3 \pmod{7^3}$, knowing that $7 \nmid ab$.

Published on 31 Jul 2020 - 21:01

score 51 · Answer 15 · 2020-08-09 12:18:34

51

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Exercise 0.17 in Miles Reid's Commutative Algebra

Published on 09 Aug 2020 - 12:18

List Question

For Eisenstein numbers $a + b\frac{1+\sqrt{3} i}{2}$ with $0 \le a, b \le n$ how can I efficiently identify all of the primes?

Eisenstein Integers modulo $(1-\omega)^2$

$\exists X, Y, Z \in \mathbb{Z}[\omega]$ such that $X^3 + Y^3 + Z^3 = \omega$?

Automorphism groups of $\mathbf Z$, $\mathbf Z[i]$, $\mathbf Z[\omega]$

Let $\pi \in \mathbb{Z}[\omega]$ be a prime. Then $\frac{\mathbb{Z}[\omega]}{\pi \mathbb{Z}[\omega]}$ has $N(\pi)$ elements

Eisenstein integers with norm value of 5

Cubic non-residue calculation

Law of cubic reciprocity for a primary prime of norm 3

Eisenstein Integers

Natural generalizations of Gaussian & Eisenstein integers?

On proving that $\mathbb{Z}[\omega]$ is a Euclidean domain.

Understanding a congruence relation in $\mathbb{Z}[\omega]$

Primes congruent to 1 mod 6

How to find all solutions for : $a^3 \equiv b^3 \pmod{7^3}$, knowing that $7 \nmid ab$.

Exercise 0.17 in Miles Reid's Commutative Algebra

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