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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 ...

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

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...

A root-finding algorithm based on the iteration formula x_(n+1)=x_n-(f(x_n))/(f^'(x_n)){1+(f(x_n)f^('')(x_n))/(2[f^'(x_n)]^2)}. This method, like Newton's method, has poor ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

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 ...

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...