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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]
Higher Arithmetic: An Algorithmic Introduction to Number Theory (2008) [8] An extension of Edwards' work in Essays in Constructive Mathematics, this textbook covers the material of a typical undergraduate number theory course, [9] but follows a constructivist viewpoint in focusing on algorithms for solving problems rather than allowing purely existential solutions.
Composite number. Highly composite number; Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; Least common multiple; Euclidean algorithm; Coprime; Euclid's lemma; Bézout's identity, Bézout's lemma; Extended Euclidean algorithm; Table of divisors; Prime number, prime power. Bonse's inequality; Prime factor. Table of ...
The NTF funds the Selfridge prize awarded at each Algorithmic Number Theory Symposium (ANTS) [2] [3] and is a regular supporter of several conferences and organizations in number theory, including the Canadian Number Theory Association (CNTA), [4] [5] Women in Numbers (WIN), and the West Coast Number Theory (WCNT) conference. [1]
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in base 10:
Ray Solomonoff (July 25, 1926 – December 7, 2009) [1] [2] was an American mathematician who invented algorithmic probability, [3] his General Theory of Inductive Inference (also known as Universal Inductive Inference), [4] and was a founder of algorithmic information theory. [5]
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic ...