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Pages in category "Number theoretic algorithms" The following 25 pages are in this category, out of 25 total. This list may not reflect recent changes. A.
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. [1]
Let be a cyclic group of order , and given ,, and a partition =, let : be the map = {and define maps : and : by (,) = {() + (,) = {+ ()input: a: a generator of G b: an element of G output: An integer x such that a x = b, or failure Initialise i ← 0, a 0 ← 0, b 0 ← 0, x 0 ← 1 ∈ G loop i ← i + 1 x i ← f(x i−1), a i ← g(x i−1, a i−1), b i ← h(x i−1, b i−1) x 2i−1 ← ...
Composite number. Highly composite number; Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; Least common multiple; Euclidean algorithm; Coprime
This section has a simplified version of the algorithm, showing how to compute the product of two natural numbers ,, modulo a number of the form +, where = is some fixed number. The integers a , b {\displaystyle a,b} are to be divided into D = 2 k {\displaystyle D=2^{k}} blocks of M {\displaystyle M} bits, so in practical implementations, it is ...
The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. [ 1 ] [ 2 ] Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p , it is in fact a ...
3.4 Number theoretic algorithms. 3.5 Numerical algorithms. ... CYK algorithm: an O(n 3) algorithm for parsing context-free grammars in Chomsky normal form;
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv n{\pmod {p}},} where x , n ∈ F p {\displaystyle x,n\in \mathbf {F} _{p}} , so n is the square of x , and where p {\displaystyle p} is an odd prime .