query: Given three polynomials $a(x), b(x)$, and $c(x)$ satisfying $\gcd(a(x), b(x), c(x))=1$
positive_passages.docid: 25229
positive_passages.text: Can any set of $n$ relatively prime elements be extended to an invertible matrix?
negative_passages.docid: 113641
negative_passages.text: Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
negative_passages.docid: 120459
negative_passages.text: Problem with finding the GCD in the Field of Polynomials mod p
negative_passages.docid: 3694
negative_passages.text: Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
negative_passages.docid: 69279
negative_passages.text: If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
negative_passages.docid: 129653
negative_passages.text: Solving a polynomial with grouping
negative_passages.docid: 87013
negative_passages.text: If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
negative_passages.docid: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
negative_passages.docid: 73391
negative_passages.text: Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
negative_passages.docid: 37808
negative_passages.text: Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
negative_passages.docid: 38404
negative_passages.text: Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
negative_passages.docid: 1713
negative_passages.text: number theory $\gcd(a,bc)=\gcd(a,c)$
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 110313
negative_passages.text: Prove that $\gcd(f(x),g(x)) = 1$.
negative_passages.docid: 156641
negative_passages.text: Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
negative_passages.docid: 24499
negative_passages.text: Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
negative_passages.docid: 39621
negative_passages.text: Let a, b, c, d be rational numbers...