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In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. [1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. [2] One says also a is prime to b or a ...
If p, q, and r are pairwise relatively prime positive integers then the link of the singularity x p + y q + z r = 0 (in other words, the intersection of a small 3-sphere around 0 with this complex surface) is a Brieskorn manifold that is a homology 3-sphere, called a Brieskorn 3-sphere Σ(p, q, r).
The elementary divisors can be obtained from the list of invariant factors of the module by decomposing each of them as far as possible into pairwise relatively prime (non-unit) factors, which will be powers of irreducible elements.
As a result, for every set of relatively prime numbers {, …,} there exists a value of such that every larger number is representable as a linear combination of {, …,} in at least one way. This consequence of the theorem can be recast in a familiar context considering the problem of changing an amount using a set of coins.
In mathematics, Legendre's equation is a Diophantine equation of the form: + + = The equation is named for Adrien-Marie Legendre who proved it in 1785 that it is solvable in integers x, y, z, not all zero, if and only if −bc, −ca and −ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, square-free, pairwise relatively prime integers and also not all ...
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1).
But in such a large, complex market, items frequently fall through the cracks, so if you do discover a counterfeit item in your Amazon Prime box, Dimyan suggests two actions. "Utilize Amazon's ...
The previous result says that a solution exists if and only if gcd(a, m) = 1, that is, a and m must be relatively prime (i.e. coprime). Furthermore, when this condition holds, there is exactly one solution, i.e., when it exists, a modular multiplicative inverse is unique: [ 8 ] If b and b' are both modular multiplicative inverses of a respect ...