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15
157
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Solving $x^2+100=y^3$ in $\mathbb{Z}^2$

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#number-theory #diophantine-equations #gaussian-integers
106
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Cardinality of associate classes in quotient ring of Gaussian integers.

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#abstract-algebra #ring-theory #integral-domain #dedekind-domain #gaussian-integers
96
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The ring $\mathbb{Z}[i]/(2)$

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#abstract-algebra #ring-theory #gaussian-integers
65
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Prime elements associate in $\mathbb{Z}[i]$

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#ring-theory #gaussian-integers
249
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If $p$ is not sum of two squares then $p$ is a prime in $\mathbb{Z}[i]$

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#prime-factorization #gaussian-integers
347
Views

Gaussian Integers and Finite Fields

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#abstract-algebra #number-theory #finite-fields #gaussian-integers
33
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A question about Gaussian primes generated by the function $w(z)=z^2+i$

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#number-theory #complex-numbers #gaussian-integers
480
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Primes congruent to $1$ mod $4$ are sum of two squares

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#elementary-number-theory #square-numbers #gaussian-integers
115
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Order in gaussian integer moduli

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#elementary-number-theory #complex-numbers #modular-arithmetic #gaussian-integers
145
Views

Power of Gaussian integer an integer

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#elementary-number-theory #gaussian-integers
809
Views

Minimal Polynomial of $1+i$ over $\Bbb Q$

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#field-theory #extension-field #minimal-polynomials #splitting-field #gaussian-integers
281
Views

Show that it is impossible to draw an equilateral triangle such that all three vertices are Gaussian integers.

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#geometry #elementary-number-theory #complex-numbers #solution-verification #gaussian-integers
295
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Quotient groups of the Gaussian integers of the form $\mathbb{Z}[i]/ c\mathbb{Z}[i]$

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#group-theory #cyclic-groups #quotient-group #gaussian-integers
146
Views

What is the structure of $\mathbb Z[i]/\mathfrak p$ where $\mathfrak p$ is a prime.

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#abstract-algebra #ring-theory #commutative-algebra #gaussian-integers #euclidean-domain
60
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Show that $\mathbb{Z}[i]=\{m+in\colon\; m,n\in\mathbb{Z}\}$ is a P.I.D

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#abstract-algebra #number-theory #principal-ideal-domains #gaussian-integers

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