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Product of $(4k-1)$ primes can't be sum of 2 squares

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#number-theory #sums-of-squares #formal-proofs #gaussian-integers
236
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Exercise about primes in the ring of Gaussian integers

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#abstract-algebra #group-theory #proof-writing #prime-numbers #gaussian-integers
216
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Value for sum of inverse of Gaussian integers

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#complex-numbers #integer-lattices #gaussian-integers
347
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Square and cubic root of gaussian Integer

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#radicals #gaussian-integers
412
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How to show that the kernel of this ring homomorphism $\phi: \mathbb{Z}[i]\to\mathbb{Z}/5\mathbb{Z}$ is the principal ideal $(2+i)$?

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#abstract-algebra #ring-theory #gaussian-integers
124
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How to count the number of elements in $(\mathbb{Z}[i]/I^{2014})\otimes_{\mathbb{Z}[i]}(\mathbb{Z}[i]/J^{2014})$?

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#commutative-algebra #modules #ideals #tensor-products #gaussian-integers
226
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Parameterization of Equation with Gaussian Integer

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#quadratics #gaussian-integers
127
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Finding an explicit map associated with the quotient ring of Gaussian integers

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#abstract-algebra #ring-theory #gaussian-integers
241
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Show that if $\beta \mid \alpha$ in $\mathbb Z[i]$ then $N(\beta) \mid N(\alpha)$

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#abstract-algebra #prime-numbers #divisibility #normed-spaces #gaussian-integers
944
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Meaning of "up to associates" in unique prime factorization

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#abstract-algebra #gaussian-integers
3.5k
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Where is wrong with this fake proof that Gaussian integer is a field?

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#fake-proofs #gaussian-integers
622
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Modular inverse of Gaussian Integers

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#finite-fields #gcd-and-lcm #gaussian-integers
55
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Factorization of the ring $\mathbb{Z} [i]$ of Gaussian Integers

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#abstract-algebra #ring-theory #gaussian-integers
98
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A way of dividing in $\mathbb{Z}[i]$

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#complex-numbers #gaussian-integers
590
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Prove $(5-i,13)$ is a principal ideal in $\mathbb{Z}[i]$

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#abstract-algebra #ring-theory #gaussian-integers

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