| Autore |
Silverman Joseph H. <1955->
|
| Edizione | [Fourth, Pearson new international edition.] |
| Pubbl/distr/stampa |
Harlow, England : , : Pearson, , [2014]
|
| Descrizione fisica |
1 online resource (459 pages) : illustrations
|
| Disciplina |
512.7
|
| Collana |
Pearson custom library
|
| Soggetto topico |
Number theory
|
| ISBN |
1-292-05541-3
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
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 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.
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| Record Nr. | UNINA-9910153066003321 |
Info
A friendly introduction to number theory / / Joseph H. Silverman
