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Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

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 ...

The square root method is an algorithm which solves the matrix equation Au=g (1) for u, with A a p×p symmetric matrix and g a given vector. Convert A to a triangular matrix ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

The symmetric successive overrelaxation (SSOR) method combines two successive overrelaxation method (SOR) sweeps together in such a way that the resulting iteration matrix is ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

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

A collection B of subsets of a set X forming a topological basis.

A finite geometry is a geometry with a finite number of points. When confined to a plane, all finite geometries are either projective plane geometries (with no parallel ...