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 (numbers), the...

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...

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...

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

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

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

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

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

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

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...

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...

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...

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...

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...

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

more of the unknowns must be an integer then it is classified in integer programming. A linear programming algorithm can solve such a problem if it can...

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...

kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced...

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...

"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...

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

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...

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

Fürer's algorithm: an integer multiplication algorithm for very large numbers possessing a very low asymptotic complexity Karatsuba algorithm: an efficient...