query: Prove $Z[\sqrt{7}]$ is euclidean domain
positive_passages.docid: 148804
positive_passages.text: Norm-Euclidean rings?
negative_passages.docid: 236
negative_passages.text: Proof of general Euclid's Lemma in a UFD (by Euclidean algorithm?)
negative_passages.docid: 53349
negative_passages.text: Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
negative_passages.docid: 122415
negative_passages.text: How to show every field is a Euclidean Domain.
negative_passages.docid: 72144
negative_passages.text: Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
negative_passages.docid: 17161
negative_passages.text: Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
negative_passages.docid: 133636
negative_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 52157
negative_passages.text: Prove that $d(n)\leq 2\sqrt{n}$
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 66238
negative_passages.text: Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 44307
negative_passages.text: Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
negative_passages.docid: 121845
negative_passages.text: Quotient of polynomials, PID but not Euclidean domain?
negative_passages.docid: 90276
negative_passages.text: Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
negative_passages.docid: 156766
negative_passages.text: Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
negative_passages.docid: 47975
negative_passages.text: Closed cone in the euclidean space $\mathbb{R}^n$
negative_passages.docid: 140409
negative_passages.text: Prove that $\sqrt{n} > \ln n$