# A Friendly Introduction to Number Theory, 4th Edition

## Book Description

* A Friendly Introduction to Number Theory, Fourth Edition* is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facetâ€”number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

### Table of Contents

Chapter 1 What Is Number Theory?

Chapter 2 Pythagorean Triples

Chapter 3 Pythagorean Triplesand the Unit Circle

Chapter 4 Sums of Higher Powers and Fermat's Last Theorem

Chapter 5 Divisibility and the Greatest Common Divisor

Chapter 6 Linear Equations and the Greatest Common Divisor

Chapter 7 Factorization and the Fundamental Theoremof Arithmetic

Chapter 8 Congruences

Chapter 9 Congruences, Powers, and Fermat's Little Theorem

Chapter 10 Congruences, Powers, and Euler's Formula

Chapter 11 Euler's Phi Function and the Chinese Remainder Theorem

Chapter 12 Prime Numbers

Chapter 13 Counting Primes

Chapter 14 Mersenne Primes

Chapter 15 Mersenne Primes and Perfect Numbers

Chapter 16 Powers Modulo m and Successive Squaring

Chapter 17 Computing kth Roots Modulo m

Chapter 18 Powers, Roots, and ''Unbreakable'' Codes

Chapter 19 Primality Testing and Carmichael Numbers

Chapter 20 Squares Modulo p

Chapter 21 Is -1 a Square Modulo p? Is 2?

Chapter 22 Quadratic Reciprocity

Chapter 23 Proof of Quadratic Reciprocity

Chapter 24 Which Primes Are Sums of Two Squares?

Chapter 25 Which Numbers Are Sums of Two Squares?

Chapter 26 As Easy as One, Two, Three

Chapter 27 Euler's Phi Function and Sums of Divisors

Chapter 28 Powers Modulo pand Primitive Roots

Chapter 29 Primitive Roots and Indices

Chapter 30 The Equation X4 + Y4 =Z4

Chapter 31 Square-Triangular Numbers Revisited

Chapter 32 Pell's Equation

Chapter 33 Diophantine Approximation

Chapter 34 Diophantine Approximation and Pell's Equation

Chapter 35 Number Theory and Imaginary Numbers

Chapter 36 The Gaussian Integers and Unique Factorization

Chapter 37 Irrational Numbers and Transcendental Numbers

Chapter 38 Binomial Coefficients and Pascal's Triangle

Chapter 39 Fibonacci's Rabbits and Linear Recurrence Sequences

Chapter 40 Oh, What a Beautiful Function

Chapter 41 Cubic Curves and Elliptic Curves

Chapter 42 Elliptic Curves with Few Rational Points

Chapter 43 Points on Elliptic Curves Modulo p

Chapter 44 Torsion Collections Modulo pand Bad Primes

Chapter 45 Defect Bounds and Modularity Patterns

Chapter 46 Elliptic Curves and Fermat's Last Theorem

## Book Details

- Title: A Friendly Introduction to Number Theory, 4th Edition
- Author: Joseph H. Silverman
- Length: 432 pages
- Edition: 4
- Language: English
- Publisher: Pearson
- Publication Date: 2012-01-28
- ISBN-10: 0321816196
- ISBN-13: 9780321816191

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