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Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then ...

An unordered factorization is a factorization of a number into a product of factors where order is ignored. The following table lists the unordered factorizations of the ...

A factorization algorithm which works by expressing N as a quadratic form in two different ways. Then N=a^2+b^2=c^2+d^2, (1) so a^2-c^2=d^2-b^2 (2) (a-c)(a+c)=(d-b)(d+b). (3) ...

A prime factorization algorithm in which a sequence of trial divisors is chosen using a quadratic sieve. By using quadratic residues of N, the quadratic residues of the ...

The second part of Pollard rho factorization method concerns detection of the fact that a sequence has become periodic. Pollard's original suggestion was to use the idea ...

Also known as the difference of squares method. It was first used by Fermat and improved by Gauss. Gauss looked for integers x and y satisfying y^2=x^2-N (mod E) for various ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

Direct search factorization is the simplest (and most simple-minded) prime factorization algorithm. It consists of searching for factors of a number by systematically ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

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 ...