Secure Checkout

Friendly Introduction to Number Theory, A (Classic Version), 4th edition

  • Joseph H. Silverman

Your access includes:

  • Search, highlight, and take notes
  • Easily create flashcards
  • Use the app for access anywhere
  • 14-day refund guarantee

$10.99per month

4-month term, pay monthly or pay $43.96

Looking for your MyLab or Mastering eTextbook? Find it hereOpens in an new tab

Learn more, spend less

  • Special partners and offers

    Enjoy perks from special partners and offers for students

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

  • Easily continue access

    Keep learning with auto-renew

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 real-life applications of mathematics.

Published by Pearson (May 24th 2023) - Copyright © 2023

ISBN-13: 9780137981175

Subject: Advanced Math

Category: Number Theory

Table of contents

Preface

Flowchart of Chapter Dependencies

Introduction

  1. What Is Number Theory?
  2. Pythagorean Triples
  3. Pythagorean Triples and the Unit Circle
  4. Sums of Higher Powers and Fermat’s Last Theorem
  5. Divisibility and the Greatest Common Divisor
  6. Linear Equations and the Greatest Common Divisor
  7. Factorization and the Fundamental Theorem of Arithmetic
  8. Congruences
  9. Congruences, Powers, and Fermat’s Little Theorem
  10. Congruences, Powers, and Euler’s Formula
  11. Euler’s Phi Function and the Chinese Remainder Theorem
  12. Prime Numbers
  13. Counting Primes
  14. Mersenne Primes
  15. Mersenne Primes and Perfect Numbers
  16. Powers Modulo m and Successive Squaring
  17. Computing kth Roots Modulo m
  18. Powers, Roots, and “Unbreakable” Codes
  19. Primality Testing and Carmichael Numbers
  20. Squares Modulo p
  21. Is -1 a Square Modulo p? Is 2?
  22. Quadratic Reciprocity
  23. Proof of Quadratic Reciprocity
  24. Which Primes Are Sums of Two Squares?
  25. Which Numbers Are Sums of Two Squares?
  26. As Easy as One, Two, Three
  27. Euler’s Phi Function and Sums of Divisors
  28. Powers Modulo p and Primitive Roots
  29. Primitive Roots and Indices
  30. The Equation X4 + Y4 = Z4
  31. Square - Triangular Numbers Revisited
  32. Pell’s Equation
  33. Diophantine Approximation
  34. Diophantine Approximation and Pell’s Equation
  35. Number Theory and Imaginary Numbers
  36. The Gaussian Integers and Unique Factorization
  37. Irrational Numbers and Transcendental Numbers
  38. Binomial Coefficients and Pascal’s Triangle
  39. Fibonacci’s Rabbits and Linear Recurrence Sequences
  40. Oh, What a Beautiful Function
  41. Cubic Curves and Elliptic Curves
  42. Elliptic Curves with Few Rational Points
  43. Points on Elliptic Curves Modulo p
  44. Torsion Collections Modulo p and Bad Primes
  45. Defect Bounds and Modularity Patterns
  46. Elliptic Curves and Fermat’s Last Theorem
  47. The Topsy-Turvey World of Continued Fractions [online]
  48. Continued Fractions, Square Roots, and Pell’s Equation [online]
  49. Generating Functions [online]
  50. Sums of Powers [online]

Further Reading

Index

A. Factorization of Small Composite Integers [online]

B. A List of Primes [online]

Your questions answered

Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.

A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.

Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.

Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.

When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.

When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.

We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.