Theory of Numbers
By: Amin Witno
Edition: 1st ed.
Publisher: BookSurge
Published: 2008
Place of publication: North Charleston, SC
Language: eng
Number of pages: 136
Subjects: Number theory; Number theory -- Data processing
Description: Theory of Numbers is a carefully written textbook for an elementary number theory course with minimal prerequisites. It begins with the classical theory of divisibility, primes, and modular arithmetic; and ends with computational topics of factorization, pseudoprimes, and primality testing. Ideal for self-study or for a one-semester course, the relatively small, measured contents include numerous exercises strategically dispersed throughout the text in order to retain theoretical context and reinforce understanding. As an extended workout, every chapter concludes with a partially guided project touching on a wide range of problems, from the old sums-of-squares theorems to the more recent cryptographical protocols.
Notes: Includes bibliographical references (p. 130-132) and index.
Table of contents: label: 1
title: Divisibility
pagenum: 1; label: 2
title: Prime Numbers
pagenum: 12; label: 3
title: Modular Arithmetic
pagenum: 21; label: 4
title: Exponentiation
pagenum: 31; label: 5
title: Primitive Roots
pagenum: 43; label: 6
title: Quadratic Residues
pagenum: 52; label: 7
title: Factorization
pagenum: 63; label: 8
title: Pseudoprime Composites
pagenum: 74; label: 9
title: Primality Proving
pagenum: 84; label: A
title: Mathematical Induction
pagenum: 96; label: B
title: Binomial Coefficients
pagenum: 98; label: C
title: Primitive Root Theorem
pagenum: 101; label: D
title: Modular Square Roots
pagenum: 103; label: E
title: Rabin's Probabilistic Test
pagenum: 108; label: F
title: Testing Primes with Lucas Sequences
pagenum: 110; title: Answers & Hints
pagenum: 115; title: Primes < 10^4
pagenum: 124; title: Pseudoprimes < 10^7
pagenum: 127; title: Bibliography
pagenum: 130; title: Notation
pagenum: 133; title: Index
pagenum: 134