Title Details: | |
Integer Factorization |
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Authors: |
Poulakis, Dimitrios |
Reviewer: |
Tzanakis, Nikolaos |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > COMPUTATIONAL NUMBER THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS AND COMPUTER SCIENCE > > |
Keywords: |
Computational Number Theory
Continuous Fractions |
Description: | |
Abstract: |
Chapter 2 is devoted to the theory of continuous fractions. More precisely, we study the presentation of the rational in finite continuous fraction and the presentation of irrationals in infinite continuous fractions. We prove that the sequence of convergent fractions of the infinitefraction of an irrational number converges to this number and we give a sufficient condition for a rational number to be a convergent fraction of the continuous fraction of a number. Furthermore, we prove that a quadratic irrational if and only if the sequence of the terms of its continuous fraction is periodic.
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Table of Contents: |
Chapter 2 contains the following sections:
2.1 Finite Continuous Fractions 2.2 Infinite Continuous Fractions 2.2 Approximation of an irrational by rationnals 2.4 Quadratic Irrationals 2.5 Exercices Bibliography |
Technical Editors: |
Karakostas, Anastasios |
Type: |
Chapter |
Creation Date: | 2015 |
Item Details: | |
License: |
Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
Handle | http://hdl.handle.net/11419/1052 |
Bibliographic Reference: | Poulakis, D. (2015). Integer Factorization [Chapter]. In Poulakis, D. 2015. Computational Number Theory [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1052 |
Language: |
Greek |
Is Part of: |
Computational Number Theory |
Number of pages |
21 |
Publication Origin: |
Kallipos, Open Academic Editions |