query: Euclidean GCD and why does it work?
positive_passages.docid: 190
positive_passages.text: Why $\gcd(qb+r,b)=\gcd(b,r)$?
negative_passages.docid: 25526
negative_passages.text: How to use the Extended Euclidean Algorithm manually?
negative_passages.docid: 26641
negative_passages.text: Problem about the definition of Euclidean domain
negative_passages.docid: 107914
negative_passages.text: Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
negative_passages.docid: 76507
negative_passages.text: $\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
negative_passages.docid: 48452
negative_passages.text: Proof that $\gcd$ divides $\operatorname{lcm}$
negative_passages.docid: 94722
negative_passages.text: GCD expressed with irreducible elements in a unique factorization domain
negative_passages.docid: 138178
negative_passages.text: Proving the number of iterations in the Euclidean algorithm
negative_passages.docid: 83871
negative_passages.text: GCDs in integral domains are unique up to unit factors (associates)
negative_passages.docid: 5789
negative_passages.text: $ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
negative_passages.docid: 37808
negative_passages.text: Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
negative_passages.docid: 62959
negative_passages.text: How to find GCD, LCM on a set of numbers
negative_passages.docid: 102133
negative_passages.text: Prove: $\gcd(a,b) = \gcd(a, b + at)$.
negative_passages.docid: 63965
negative_passages.text: How can I compute the sum of $ {m\over\gcd(m,n)}$?
negative_passages.docid: 95533
negative_passages.text: I need some help with a GCD and LCM's Problem
negative_passages.docid: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
negative_passages.docid: 149993
negative_passages.text: Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).