precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists with coefficients...

the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number...

general algorithm for integer factorization, any integer can be factored into its constituent prime factors by repeated application of this algorithm. The...

Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also...

The algorithm can be used to find integer solutions to many problems. In particular, the LLL algorithm forms a core of one of the integer relation algorithms...

Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and...

The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a...

(reciprocal) licenses: MINTO (Mixed Integer Optimizer, an integer programming solver which uses branch and bound algorithm) has publicly available source code...

optimal bound, although this remains a conjecture today. Integer multiplication algorithms can also be used to multiply polynomials by means of the method...

Let y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt...

The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen...

(GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with...

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...

A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or...

empty_list for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } Using an integer factorization algorithm optimized for smooth numbers, try to factor g k mod q {\displaystyle...

Gaussian integers share many properties with integers: they form a Euclidean domain, and thus have a Euclidean division and a Euclidean algorithm; this implies...

theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by...

discrete logarithms in a finite abelian group whose order is a smooth integer. The algorithm was introduced by Roland Silver, but first published by Stephen...

Institute Relation Locator) is a hypothetical hardware device designed to speed up the sieving step of the general number field sieve integer factorization...

Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning...

of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest...

"ABC ABCDAB ABCDABCDABDE". At any given time, the algorithm is in a state determined by two integers: m, denoting the position within S where the prospective...

with the AKS algorithm. The AKS primality test is based upon the following theorem: Given an integer n ≥ 2 {\displaystyle n\geq 2} and integer a {\displaystyle...

to many digits, and then using an integer relation-finding algorithm (typically Helaman Ferguson's PSLQ algorithm) to find a sequence A that adds up...

binary relation Traveling salesman problem Christofides algorithm Nearest neighbour algorithm Vehicle routing problem Clarke and Wright Saving algorithm Warnsdorff's...

conquer), its running time is described by a recurrence relation. A simple example is the time an algorithm takes to find an element in an ordered vector with...

plane methods that is used extensively for solving integer linear programs. Evolutionary algorithm Alpha–beta pruning A. H. Land and A. G. Doig (1960)...

following algorithm (for a zero-based array). -- To shuffle an array a of n elements (indices 0..n-1): for i from n−1 down to 1 do j ← random integer such...

degree of precision – typically 100 significant figures or more. Integer relation algorithms are then used to search for relations between these values and...

of distinct integers AND the integers are all in S AND the integers sum to 0 THEN OUTPUT "yes" and HALT This is a polynomial-time algorithm accepting an...