particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is...

In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the...

the concept of a maximal common divisor is needed to generalize greatest common divisors to number systems in which the common divisors of a set of elements...

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...

having zero divisors. The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block...

the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity...

common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors,...

N(d) of the greatest common divisor of a and b is a common divisor of N(a), N(b), and N(a + b). When the greatest common divisor D of these three integers...

is principal, which shows that any Weil divisor is linearly equivalent to some power of a hyperplane divisor. This consideration proves that the Picard...

to the set of its prime divisors. It is order-preserving: if x divides y, then each prime divisor of x is also a prime divisor of y. However, it is neither...

divisor number, 5 × 21638 - 1 is prime 1639 = nonagonal number 1640 = pronic number 1641 = 412 - 41 + 1 = H41 (the 41st Hogben number) 1642 = maximal...

The set of taps is setwise co-prime; i.e., there must be no divisor other than 1 common to all taps. Tables of primitive polynomials from which maximum-length...

Jefferson's method is the unique divisor method satisfying the lower quota rule. Javascript demo of several common apportionment rules Proportional representation...

nonzero constant, the constant d is a common divisor in S of a and b; we shall show it is in fact a greatest common divisor by showing that it lies in aS +...

polynomial with integer coefficients that is a divisor of x n − 1 {\displaystyle x^{n}-1} and is not a divisor of x k − 1 {\displaystyle x^{k}-1} for any...

237,510 = harmonic divisor number 238,591 = number of free 13-ominoes 241,920 = highly totient number 242,060 = harmonic divisor number 248,832 = 125...

bases. The Euclidean algorithm for computing the polynomial greatest common divisor is a special case of Buchberger's algorithm restricted to polynomials...

Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be...

The highest averages, divisor, or divide-and-round methods are a family of apportionment rules, i.e. algorithms for fair division of seats in a legislature...

meet and the join of a and b are given by the greatest common divisor (gcd) and the least common multiple (lcm) of a and b, respectively. The ring addition...

the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic...

to have an aliquot sum of 144 = 122. Only three numbers have a set of divisors that generate a sum equal to 90, they are 40, 58, and 89. 90 is also the...

division with remainder, for example, Euclid's algorithm for the greatest common divisor. Gaussian integer Eisenstein integer The icosians The Lie group F4 The...

F(n)=F\otimes _{{\mathcal {O}}_{X}}{\mathcal {O}}_{X}(n).} 2.  If D is a Cartier divisor and F is an O X {\displaystyle {\mathcal {O}}_{X}} -module (X arbitrary)...

the quota is called a "divisor". For a given value of the divisor, the population count for each region is divided by this divisor and then rounded to give...

Euclidean Algorithm Generates Traditional Musical Rhythms". The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences...

of f, and the greatest common divisor of two polynomials is independent of the ambient field, so the greatest common divisor of f and f′ has coefficients...

polynomial greatest common divisor of two polynomials. Here, "greatest" means "having a maximal degree" or, equivalently, being maximal for the preorder...

the restrictions noted. The notation (a,b) represents the greatest common divisor of the integers a and b. Simplicity: Simple for p a prime number. Order:...

divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic...