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

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

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

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...

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

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

The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a divide-and-conquer...

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...

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...

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

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...

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

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...

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

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...

calculated through the Euclidean algorithm, since lcm(a, b) = ⁠|ab|/gcd(a, b)⁠. λ(n) is kept secret. Choose an integer e such that 1 < e < λ(n) and gcd(e...

if there is an integer k such that a − b = k m. Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible...

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field...

exponential-time algorithm, practical only for small groups G. More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization...

Ramanujan–Sato series. In 2006, mathematician Simon Plouffe used the PSLQ integer relation algorithm to generate several new formulae for π, conforming to the following...

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

computational problem equivalent to integer factorization. An equivalent, but slightly more redundant version of this algorithm was developed by Alberto Tonelli...

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...

integer values are superficial, i.e., the solutions satisfy these restrictions anyway. In the general case, a specialized algorithm or an algorithm that...

"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...

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...