A friendly introduction to number theory. (2013)
- Record Type:
- Book
- Title:
- A friendly introduction to number theory. (2013)
- Main Title:
- A friendly introduction to number theory
- Further Information:
- Note: Joseph H. Silverman, Brown University.
- Authors:
- Silverman, Joseph H, 1955-
- Contents:
- Cover -- Table of Contents -- 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 and 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. Square-Triangular 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 andCover -- Table of Contents -- 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 and 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. Square-Triangular 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 -- 44. The Topsy-Turvy World of Continued Fractions -- 45. Continued Fractions and Pell's Equation -- 46. Generating Functions -- 47. Sums of Powers -- 48. Appendix: A List of Primes -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z … (more)
- Edition:
- Fourth edition
- Publisher Details:
- Harlow, United Kingdom : Pearson
- Publication Date:
- 2013
- Extent:
- 1 online resource (472 pages)
- Subjects:
- 512.7
Number theory -- Textbooks
Number theory
Electronic books
Textbooks - Languages:
- English
- ISBNs:
- 9781292055411
1292055413 - Related ISBNs:
- 9781292027098
1292027096 - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.724772
- Ingest File:
- 14_046.xml