query: Euclidean Domain and Divison Algorithm
positive_passages.docid: 18887
positive_passages.text: Euclidean domain in which the quotient and remainder are always unique
negative_passages.docid: 108898
negative_passages.text: An Analogue of CRT for Polynomial Ring
negative_passages.docid: 102914
negative_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 43103
negative_passages.text: Unique factorization domain and principal ideals
negative_passages.docid: 157572
negative_passages.text: The distance between two sets inside euclidean space
negative_passages.docid: 55259
negative_passages.text: ArcTan[z] and ArcTan[x,y], Restriction and Conversion
negative_passages.docid: 134539
negative_passages.text: Euclidean and induction with prime numbers
negative_passages.docid: 146470
negative_passages.text: Show $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain
negative_passages.docid: 27652
negative_passages.text: metric on the Euclidean Group
negative_passages.docid: 124295
negative_passages.text: Divison and remainder in Prolog
negative_passages.docid: 75764
negative_passages.text: Regularity of a domain - definition
negative_passages.docid: 153069
negative_passages.text: Proof for Unique Factorization Domain
negative_passages.docid: 19822
negative_passages.text: For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?
negative_passages.docid: 84751
negative_passages.text: How can it be possible to localize a ring at a set with zero divisors?
negative_passages.docid: 107349
negative_passages.text: Working with elementary type proofs of divisor functions
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 9118
negative_passages.text: Polynomial division: an obvious trick? [reducing mod $\textit{simpler}$ multiples]