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A friendly introduction to number theory

Author: Joseph H Silverman
Publisher: Upper Saddle River, New Jersey : Pearson Prentice Hall, ©2006.
Edition/Format:   Print book : English : 3rd edView all editions and formats

Aimed at courses in Elementary Number Theory, this book is for math majors, for mathematics education students, and for Computer Science students. Starting from basic algebra, it takes the reader to  Read more...


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Genre/Form: Textbooks
Additional Physical Format: Online version:
Silverman, Joseph H., 1955-
Friendly introduction to number theory.
Upper Saddle River, New Jersey : Pearson Prentice Hall, ©2006
Document Type: Book
All Authors / Contributors: Joseph H Silverman
ISBN: 0131861379 9780131861374
OCLC Number: 57405517
Description: vii, 434 pages : illustrations ; 24 cm
Contents: 1. What Is Number Theory? 2. Pythagorean Triples3. Pythagorean Triples and the Unit Circle 4. Sums of Higher Powers and Fermat's Last Theorem5. Divisibility and the Greatest Common Divisor 6. Linear Equations and the Greatest Common Divisor7. Factorization and the Fundamental Theorem of Arithmetic 8. Congruences9. Congruences, Powers, and Fermat's Little Theorem10. Congruences, Powers, and Euler's Formula11. Euler's Phi Function and the Chinese Remainder Theorem12. Prime Numbers13. Counting Primes14. Mersenne Primes15. Mersenne Primes and Perfect Numbers816. Powers Modulo m and Successive Squaring17. Computing kth Roots Modulo m18. Powers, Roots, and "Unbreakable" Codes19. Primality Testing and Carmichael Numbers20. Euler's Phi Function and Sums of Divisors21. Powers Modulo p and Primitive Roots22. Primitive Roots and Indices23. Squares Modulo p24. Is -1 a Square Modulo p? Is 2?25. Quadratic Reciprocity 26. Which Primes Are Sums of Two Squares?27. Which Numbers Are Sums of Two Squares?28. The Equation X4 + Y 4 = Z4 29. Square-Triangular Numbers Revisited 30. Pell's Equation31. Diophantine Approximation32. Diophantine Approximation and Pell's Equation33. Number Theory and Imaginary Numbers34. The Gaussian Integers and Unique Factorization35. Irrational Numbers and Transcendental Numbers36. Binomial Coefficients and Pascal's Triangle37. Fibonacci's Rabbits and Linear Recurrence Sequences38. Oh, What a Beautiful Function39. The Topsy-Turvy World of Continued Fractions40. Continued Fractions, Square Roots and Pell's Equation41. Generating Functions42. Sums of Powers43. Cubic Curves and Elliptic Curves44. Elliptic Curves with Few Rational Points 45. Points on Elliptic Curves Modulo p46. Torsion Collections Modulo p and Bad Primes47. Defect Bounds and Modularity Patterns48. Elliptic Curves and Fermat's Last TheoremFurther Reading A. Factorization of Small Composite IntegersB. A List of Primes
Responsibility: Joseph H. Silverman.


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