In mathematics, the greatest common divisor
(gcd) of two or more integers is the largest positive integer that divides the numbers without a remainder.
From the relationships (11) and (12) it follows that the polynomial cm(z) is the greatest common divisor
of all elements of matrix C(z).
i] have greatest common divisor
1, we have [zeta] = 1 as a pole of order N + 1, and the other poles have order strictly less.
An element b in CD(B) is a greatest common divisor
of B if and only if CD(B) = D(b).
Theorem 1 If c = a + b and d = gcd(a, b) the orbit of the billiard ball (on the corresponding table) passes through a lattice point (x, y) on the boundary if and only if d|x and d|y (gcd(a, b) denotes the greatest common divisor
of a and b)
Second, the "ideal" district size is used as a common divisor
for the population of each state, yielding what are called the states' quotas of Representatives.
where C(s) is a left greatest common divisor
of matrixes, and [?
To prove Corollary 2, note that the greatest common divisor
of 4 and 6 is (4, 6) = 2, so from Corollary 1 we have the identity
He describes rings and fields, including linear equations in a field and vector spaces, polynomials over a field, factorization into primes, ideals and the greatest common divisor
, solution of the general equation of nth degree, residual classes, extension fields, and isomorphisms.
Let denote [DELTA] the greatest common divisor
of E and F, with E = [DELTA]E and F = [DELTA][?
Finding the Greatest Common Divisor
and the Least Common Multiple is of Type [I.
In section II (24 pages) Gauss proves the uniqueness of the factorisation of integers into primes and defines the concepts of greatest common divisor
and least common multiple.