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Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals #gaussian-integers
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Quotient field of gaussian integers

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#abstract-algebra #ring-theory #fractions #gaussian-integers
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Examples of small multiplicative subgroups of BIG quotient rings of the gaussian integers

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#abstract-algebra #gaussian-integers
407
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Sums of two Gaussian Integer squares

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#number-theory #complex-numbers #sums-of-squares #gaussian-integers
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Norm of Irreducible Gaussian Integer

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#elementary-number-theory #gaussian-integers
378
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Application of Chinese Remainder Theorem to Ring Isomorphism

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#abstract-algebra #ring-theory #chinese-remainder-theorem #gaussian-integers #ring-isomorphism
159
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Sum of squares function $r_2(n)$ logarithmic moment asymptotics

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#number-theory #elementary-number-theory #gaussian-integers
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Relevant to Gaussian Integers

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#number-theory #gaussian-integers
71
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When is $\dfrac{(-1)^s-1}{i^s} \in \mathbb{Z}[i]$?

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#complex-analysis #number-theory #divisibility #gaussian-integers
80
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Quotient Fields of the Gaussian Integers

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#abstract-algebra #finite-fields #quotient-group #gaussian-integers
106
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Prove there are 4 integer roots on $x^2+y^2=2^n$

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#elementary-number-theory #circles #integers #sums-of-squares #gaussian-integers
49
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$\#ℤ[i]/\alpha\betaℤ[i] = \#ℤ[i]/\alphaℤ[i] · \#ℤ[i]/ \beta ℤ[i]$

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#abstract-algebra #ring-theory #ideals #gaussian-integers
145
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$\gcd(135-14i, 155+34i)$ with the Euclidean algorithm

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#abstract-algebra #complex-numbers #gcd-and-lcm #euclidean-algorithm #gaussian-integers
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Is there any integer solution for $\operatorname{Re}(a+bi)^n=\pm1$, where $n\geq 2$, except $(a,b)=(\pm1,0),(0,\pm1)$?

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#elementary-number-theory #complex-numbers #gaussian-integers
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Can $\operatorname{Re}(a+bi)^{n}$ be overlapped with $a,b\in\mathbb{Z}$ fixed?

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#number-theory #elementary-number-theory #complex-numbers #diophantine-equations #gaussian-integers

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