List questions from gaussian-integers

Published on 09 May 2020 - 2:53

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What is a generator for an ideal such that $I=\{a+bi|a+b \text{ is even}\}$?

Published on 11 May 2020 - 17:37

171

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If p (mod 4) = 3 and p is a Gaussian Prime. How to show that Z[i]/(p) is equal to GF(p^2)/(x^2+1)?

Published on 11 May 2020 - 19:57

218

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Use the Euclidean algorithm to find the GCD of $1 + 28i$ and $4 + 7i$

Published on 15 May 2020 - 2:36

122

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Prove an infinite product factorization of lemniscate sine

Published on 21 May 2020 - 14:10

235

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GCD of Gaussian Integers $\text{gcd}(4, 36+18i)$

Published on 09 Jun 2020 - 8:07

295

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Why does the characterization of Gaussian primes really work?

Published on 21 Jun 2020 - 21:52

234

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"vector space"-like set over non-field

Published on 01 Jul 2020 - 2:53

167

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Enumerate the elements of a quotient Gaussian Integers ring

Published on 02 Jul 2020 - 6:23

27

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Characterization of Gaussian numbers, proof explanation

Published on 02 Jul 2020 - 14:01

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How many unit squares of a square grid overlap a circle of given radius centered on the origin?

Published on 05 Jul 2020 - 19:56

191

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If $(a+bi)$ is a unit in $\mathbb{Z} [i]$, then $N(a+bi) = 1$?

Published on 16 Jul 2020 - 0:08

37

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Showing the property that norm in the ring $\mathbb{Z}[\delta]$ with $\delta=\frac{1+\sqrt{d}}{2}$, $d<0$ is multiplicative.

Published on 26 Jul 2020 - 10:20

488

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What are the unit elements in $\Bbb{Z}[i]$?

Published on 28 Jul 2020 - 2:20

142

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Gaussian Prime must have size $p$ or $p^2$

Published on 30 Jul 2020 - 2:22

List Question

Number Theory: Quadratic Fields

What is a generator for an ideal such that $I=\{a+bi|a+b \text{ is even}\}$?

If p (mod 4) = 3 and p is a Gaussian Prime. How to show that Z[i]/(p) is equal to GF(p^2)/(x^2+1)?

Use the Euclidean algorithm to find the GCD of $1 + 28i$ and $4 + 7i$

Prove an infinite product factorization of lemniscate sine

GCD of Gaussian Integers $\text{gcd}(4, 36+18i)$

Why does the characterization of Gaussian primes really work?

"vector space"-like set over non-field

Enumerate the elements of a quotient Gaussian Integers ring

Characterization of Gaussian numbers, proof explanation

How many unit squares of a square grid overlap a circle of given radius centered on the origin?

If $(a+bi)$ is a unit in $\mathbb{Z} [i]$, then $N(a+bi) = 1$?

Showing the property that norm in the ring $\mathbb{Z}[\delta]$ with $\delta=\frac{1+\sqrt{d}}{2}$, $d<0$ is multiplicative.

What are the unit elements in $\Bbb{Z}[i]$?

Gaussian Prime must have size $p$ or $p^2$

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