Friendly Introduction to Number Theory, A (Classic Version), 4th edition
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Overview
Hallmark features of this title
 50 short chapters provide flexibility and options for instructors and students. A flowchart of chapter dependencies is included.
 5 basic steps are emphasized throughout the text to help readers develop a robust thought process: Experimentation, pattern recognition, hypothesis formation, hypothesis testing, and formal proof.
 RSA cryptosystem, elliptic curves, and Fermat's Last Theorem are featured, showing the reallife applications of mathematics.
Published by Pearson (May 24th 2023)  Copyright © 2023
ISBN13: 9780137981175
Subject: Advanced Math
Category: Number Theory
Table of contents
Preface
Flowchart of Chapter Dependencies
Introduction
 What Is Number Theory?
 Pythagorean Triples
 Pythagorean Triples and the Unit Circle
 Sums of Higher Powers and Fermat’s Last Theorem
 Divisibility and the Greatest Common Divisor
 Linear Equations and the Greatest Common Divisor
 Factorization and the Fundamental Theorem of Arithmetic
 Congruences
 Congruences, Powers, and Fermat’s Little Theorem
 Congruences, Powers, and Euler’s Formula
 Euler’s Phi Function and the Chinese Remainder Theorem
 Prime Numbers
 Counting Primes
 Mersenne Primes
 Mersenne Primes and Perfect Numbers
 Powers Modulo m and Successive Squaring
 Computing k^{th} Roots Modulo m
 Powers, Roots, and “Unbreakable” Codes
 Primality Testing and Carmichael Numbers
 Squares Modulo p
 Is 1 a Square Modulo p? Is 2?
 Quadratic Reciprocity
 Proof of Quadratic Reciprocity
 Which Primes Are Sums of Two Squares?
 Which Numbers Are Sums of Two Squares?
 As Easy as One, Two, Three
 Euler’s Phi Function and Sums of Divisors
 Powers Modulo p and Primitive Roots
 Primitive Roots and Indices
 The Equation X^{4} + Y^{4} = Z^{4}
 Square  Triangular Numbers Revisited
 Pell’s Equation
 Diophantine Approximation
 Diophantine Approximation and Pell’s Equation
 Number Theory and Imaginary Numbers
 The Gaussian Integers and Unique Factorization
 Irrational Numbers and Transcendental Numbers
 Binomial Coefficients and Pascal’s Triangle
 Fibonacci’s Rabbits and Linear Recurrence Sequences
 Oh, What a Beautiful Function
 Cubic Curves and Elliptic Curves
 Elliptic Curves with Few Rational Points
 Points on Elliptic Curves Modulo p
 Torsion Collections Modulo p and Bad Primes
 Defect Bounds and Modularity Patterns
 Elliptic Curves and Fermat’s Last Theorem
 The TopsyTurvey World of Continued Fractions [online]
 Continued Fractions, Square Roots, and Pell’s Equation [online]
 Generating Functions [online]
 Sums of Powers [online]
Further Reading
Index
A. Factorization of Small Composite Integers [online]
B. A List of Primes [online]
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