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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 ...
We tend to focus more on the mathematics and less on the sometimes fascinat-ing algorithmic details. However, the subject is grounded in, and motivated by, examples; one can learn interesting and surprising things by actually implement-ing algorithms in number theory.
A few simple observations lead to a far superior method: Euclid’s algorithm, or the Euclidean algorithm. First, if \(d\) divides \(a\) and \(d\) divides \(b\), then \(d\) divides their difference, \(a\) - \(b\), where \(a\) is the larger of the two.
About this book. With the advent of powerful computing tools and numerous advances in math ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right.
Provides a unified introduction to elementary and analytic number theory; Includes algorithms in Python for a computational approach to number theory; Contains over 200 exercises with hints
In this chapter, we shall study the algorithmic aspects of number theory, and more specifically, we shall introduce various algorithms for solving these three types of number-theoretic problems.
A few simple observations lead to a far superior method: Euclid’s algorithm, or the Euclidean algorithm. First, if d divides a and d divides b, then d divides their difference, a - b, where a is the larger of the two.
