query: Show that $\mathbb{Z}[i]/\langle 1+4i\rangle \simeq \mathbb{Z}_{17}$
positive_passages.docid: 6121
positive_passages.text: Quotient ring of Gaussian integers
negative_passages.docid: 50241
negative_passages.text: Cardinality of the quotient ring $\mathbb Z_5[i]/\langle 1+i\rangle$
negative_passages.docid: 128566
negative_passages.text: Proving $2$ generates $(\mathbb{Z}/19\mathbb{Z})^*$ by only looking at a few powers
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 108775
negative_passages.text: Identify the ring $\mathbb {Z}[i]/(2 + i) $
negative_passages.docid: 89215
negative_passages.text: How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
negative_passages.docid: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 47522
negative_passages.text: group generators of $(\mathbb Z_{17}-\{0\},\times)$
negative_passages.docid: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 102721
negative_passages.text: Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
negative_passages.docid: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 115282
negative_passages.text: Showing that $\mathbb Q(\sqrt{17})$ has class number 1