query: GCD of polynomials over a field and its extension
positive_passages.docid: 9873
positive_passages.text: GCD in a PID persists in extension domains
negative_passages.docid: 137369
negative_passages.text: Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)
negative_passages.docid: 68753
negative_passages.text: Elements in finite field extensions
negative_passages.docid: 117098
negative_passages.text: Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
negative_passages.docid: 146617
negative_passages.text: A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
negative_passages.docid: 19500
negative_passages.text: How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 143321
negative_passages.text: Number of roots of a polynomial over a finite field
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 69935
negative_passages.text: Field extensions of finite degree and primitive elements
negative_passages.docid: 111493
negative_passages.text: Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
negative_passages.docid: 94914
negative_passages.text: Concise proof that every common divisor divides GCD without Bezout's identity?
negative_passages.docid: 126127
negative_passages.text: A field extension of prime degree
negative_passages.docid: 58490
negative_passages.text: Polynomials, finite fields and cardinality/dimension considerations
negative_passages.docid: 55719
negative_passages.text: Order of general- and special linear groups over finite fields.
negative_passages.docid: 19164
negative_passages.text: On the GCD of a Pair of Fermat Numbers
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$