In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor...

polynomials (see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below). The greatest common divisor (GCD) of integers...

their greatest common divisor. Extended Euclidean algorithm also refers to a very similar algorithm for computing the polynomial greatest common divisor and...

and greatest common divisors of such polynomials. Gauss's lemma asserts that the product of two primitive polynomials is primitive. (A polynomial with...

the Euclidean algorithm for polynomials that computes a polynomial greatest common divisor of two polynomials. Here, "greatest" means "having a maximal degree"...

nonzero polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its...

the definition of Gröbner bases. Euclidean algorithm for polynomial greatest common divisor computation and Gaussian elimination of linear systems are...

account. Other applications of multi-modular arithmetic include polynomial greatest common divisor, Gröbner basis computation and cryptography. A residue numeral...

near John Day, Oregon, United States Greatest common divisor Binary GCD algorithm Polynomial greatest common divisor Lehmer's GCD algorithm Griffith College...

who proved it for polynomials, is the following theorem: Bézout's identity — Let a and b be integers with greatest common divisor d. Then there exist...