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

• Joseph H. Silverman

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## Overview

A Friendly Introduction to Number Theory, 4th Edition introduces you to the overall themes and methodology of mathematics through the detailed study of one particular facet: number theory. Starting with nothing more than basic high school algebra, you are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for undergraduates 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.

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.

ISBN-13: 9780137981175

Category: Number Theory

## Overview

#### 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?
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]

#### B. A List of Primes [online]

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