Search Results for ""

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

Following Yates (1980), a prime p such that 1/p is a repeating decimal with decimal period shared with no other prime is called a unique prime. For example, 3, 11, 37, and ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

The elliptic curve factorization method, abbreviated ECM and sometimes also called the Lenstra elliptic curve method, is a factorization algorithm that computes a large ...