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15
57
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Residues and perfect squares in $\mathbb{Z}[i][X]$

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#abstract-algebra #number-theory #polynomials #divisibility #gaussian-integers
149
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Explicitly finding the elements of $\mathbb Z[i]/\langle 3+2i\rangle$

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#abstract-algebra #ring-theory #gaussian-integers
49
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Finding every solution of $a^2+b^2+c^2=3$ in $\mathbb{Q}(i)$

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#diophantine-equations #quadratic-forms #parametrization #gaussian-integers
60
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Using Chinese remainder theorem for Gaussian integers

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#chinese-remainder-theorem #gaussian-integers
121
Views

Proving $|ad-bc|=1$ for the Product of Two Numbers Expressible as Sums of Two Squares

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#number-theory #gaussian-integers
142
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How many units are there in $\mathbb{Z}[i]/ (13^{2021})$?

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#ring-theory #gaussian-integers
86
Views

Diophantine Equation in Gaussian Integers

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#diophantine-equations #gaussian-integers
124
Views

Proving $(x - i)$ and $(x + i)$ are coprime in $\mathbb{Z}[i]$

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#elementary-number-theory #gaussian-integers
72
Views

Complete Residue System Modulo $z$ in the Gaussian Integers

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#number-theory #modular-arithmetic #gaussian-integers
90
Views

Gaussian integers relatively prime to $9$

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#elementary-number-theory #prime-numbers #gaussian-integers
83
Views

Euler Phi Function for Gaussian integers

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#number-theory #totient-function #gaussian-integers
57
Views

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

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#ring-theory #integers #automorphism-group #gaussian-integers #eisenstein-integers
57
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What is the factorization of 26 in $\mathbb Z[i]$ into irreducible?

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#abstract-algebra #ring-theory #unique-factorization-domains #gaussian-integers
147
Views

Show that: exists unique ring homomorphism $\varphi : \mathbb{Z} [ i ] \longrightarrow R$ with $\varphi ( i ) = a$, where $a^{2} =-1_{R}$

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#abstract-algebra #ring-homomorphism #universal-property #gaussian-integers
97
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Show that the GCD of 3+4i and 7-i in Z[i] is 1

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#abstract-algebra #ring-theory #gcd-and-lcm #gaussian-integers

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