A friendly introduction to number theory
 Author/Creator
 Silverman, Joseph H., 1955
 Language
 English.
 Edition
 4th ed.
 Imprint
 Boston : Pearson, c2013.
 Physical description
 ix, 409 p. : ill ; 24 cm.
Access
Available online

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QA241 .S497 2013

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QA241 .S497 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [396]) and index.
 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. Quadratic Reciprocity 22. Proof of Quadratic Reciprocity 23. Which Primes Are Sums of Two Squares? 24. Which Numbers Are Sums of Two Squares? 25. Euler's Phi Function and Sums of Divisors 26. Powers Modulo p and Primitive Roots 27. Primitive Roots and Indices 28. The Equation X4 + Y4 = Z4 29. SquareTriangular Numbers Revisited 30. Pell's Equation 31. Diophantine Approximation 32. Diophantine Approximation and Pell's Equation 33. Number Theory and Imaginary Numbers 34. The Gaussian Integers and Unique Factorization 35. Irrational Numbers and Transcendental Numbers 36. Binomial Coefficients and Pascal's Triangle 37. Fibonacci's Rabbits and Linear Recurrence Sequences 38. Cubic Curves and Elliptic Curves 39. Elliptic Curves with Few Rational Points 40. Points on Elliptic Curves Modulo p 41. Torsion Collections Modulo p and Bad Primes 42. Defect Bounds and Modularity Patterns 43. Elliptic Curves and Fermat's Last Theorem Index *44. The TopsyTurvey World of Continued Fractions [online] *45. Continued Fractions, Square Roots, and Pell's Equation [online] *46. Generating Functions [online] *47. Sums of Powers [online] *A. A List of Primes [online] *These chapters are available online.
 (source: Nielsen Book Data)
 Publisher's Summary
 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..
(source: Nielsen Book Data)
Subjects
 Subject
 Number theory > Textbooks.
Bibliographic information
 Publication date
 2013
 Responsibility
 Joseph H. Silverman.
 ISBN
 9780321816191
 0321816196