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A number n with prime factorization n=product_(i=1)^rp_i^(a_i) is called k-almost prime if it has a sum of exponents sum_(i=1)^(r)a_i=k, i.e., when the prime factor ...

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

If {a_j} subset= D(0,1) (with possible repetitions) satisfies sum_(j=1)^infty(1-|a_j|)<=infty, where D(0,1) is the unit open disk, and no a_j=0, then there is a bounded ...

Ruffini's rule a shortcut method for dividing a polynomial by a linear factor of the form x-a which can be used in place of the standard long division algorithm. This method ...

A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

Finch (2001, 2003) defines a k-rough (or k-jagged) number to be positive integer all of whose prime factors are greater than or equal to k. Greene and Knuth define "unusual ...

For an integer n>=2, let gpf(x) denote the greatest prime factor of n, i.e., the number p_k in the factorization n=p_1^(a_1)...p_k^(a_k), with p_i<p_j for i<j. For n=2, 3, ...

Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_(ij) defined ...

The Landau-Mignotte bound, also known as the Mignotte bound, is used in univariate polynomial factorization to determine the number of Hensel lifting steps needed. It gives ...