List questions from gaussian-integers

Published on 25 Mar 2026 - 1:18

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Proving Gaussian Integers are countable

Published on 21 Mar 2017 - 2:22

258

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Prove that: Any field containing $Z[i]$ as a subring contains $Q[i]$ as a subfield.

Published on 21 Mar 2017 - 5:33

389

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Countability of Gaussian Integers

Published on 25 Mar 2017 - 16:22

33

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Why is this quotient of the Gaussian integers a field?

Published on 28 Mar 2017 - 10:45

403

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GCD in the Gaussian Integers

Published on 01 Apr 2017 - 20:55

570

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Closed form bijection between integers and pairs thereof

Published on 05 Apr 2017 - 9:09

1.6k

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Showing that $\mathbb{Z}[i]$ is not isomorphic to $\mathbb{Z}[\sqrt{2}]$

Published on 05 Apr 2017 - 16:38

62

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Investigating number of equivalence classes in the Gaussian integers formed by adding integers.

Published on 09 Feb 2023 - 17:04

240

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$\Bbb Z[i]$ is a principal ideal domain (Marcus' Number Fields, Exercise $1.7$)

Published on 11 Feb 2023 - 10:13

107

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If $p\in\mathbb{Z}$ is a prime and $p\equiv 1$ mod $4$, show that the quotient ring $\mathbb{Z}[i]/(p)$ has order $p^2$.

Published on 13 Feb 2023 - 1:01

133

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Is $SL_2(\mathbb{Z}[i])$ finitely generated?

Published on 22 Feb 2023 - 22:16

62

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Generalizations of the Gauss circle problem

Published on 25 Feb 2023 - 1:46

68

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question about gcd in Z[i] gauss integers

Published on 03 May 2023 - 13:50

57

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Calculating modular roots over Gaussian integers

Published on 23 Feb 2026 - 3:01

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How to find an upper bound on the number of solutions of $y^3=x^2+4^k$

Proving Gaussian Integers are countable

Prove that: Any field containing $Z[i]$ as a subring contains $Q[i]$ as a subfield.

Countability of Gaussian Integers

Why is this quotient of the Gaussian integers a field?

GCD in the Gaussian Integers

Closed form bijection between integers and pairs thereof

Showing that $\mathbb{Z}[i]$ is not isomorphic to $\mathbb{Z}[\sqrt{2}]$

Investigating number of equivalence classes in the Gaussian integers formed by adding integers.

$\Bbb Z[i]$ is a principal ideal domain (Marcus' Number Fields, Exercise $1.7$)

If $p\in\mathbb{Z}$ is a prime and $p\equiv 1$ mod $4$, show that the quotient ring $\mathbb{Z}[i]/(p)$ has order $p^2$.

Is $SL_2(\mathbb{Z}[i])$ finitely generated?

Generalizations of the Gauss circle problem

question about gcd in Z[i] gauss integers

Calculating modular roots over Gaussian integers

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