Higher arithmetic : an algorithmic introduction to number theory / Harold M. Edwards.

Format:

Book

Author/Creator:

Edwards, Harold M., author.

Series:

Student mathematical library ; v. 45.

The Student Mathematical Library ; v. 45

Language:

English

Subjects (All):

Number theory.

Physical Description:

1 online resource (xii, 210 pages) : illustrations.

Other Title:

Student Mathematical Library.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2008]

System Details:

text file

Contents:

Chapter 1. Numbers Chapter 2. The problem $A\square + B = \square $ Chapter 3. Congruences Chapter 4. Double congruences and the Euclidean algorithm Chapter 5. The augmented Euclidean algorithm Chapter 6. Simultaneous congruences Chapter 7. The fundamental theorem of arithmetic Chapter 8. Exponentiation and orders Chapter 9. Euler's $\phi $-function Chapter 10. Finding the order of $a\bmod c$ Chapter 11. Primality testing Chapter 12. The RSA cipher system Chapter 13. Primitive roots $\bmod \, p$ Chapter 14. Polynomials Chapter 15. Tables of indices $\bmod \, p$ Chapter 16. Brahmagupta's formula and hypernumbers Chapter 17. Modules of hypernumbers Chapter 18. A canonical form for modules of hypernumbers Chapter 19. Solution of $A\square + B = \square $ Chapter 20. Proof of the theorem of Chapter 19 Chapter 21. Euler's remarkable discovery Chapter 22. Stable modules Chapter 23. Equivalence of modules Chapter 24. Signatures of equivalence classes Chapter 25. The main theorem Chapter 26. Modules that become principal when squared Chapter 27. The possible signatures for certain values of $A$ Chapter 28. The law of quadratic reciprocity Chapter 29. Proof of the Main Theorem Chapter 30. The theory of binary quadratic forms Chapter 31. Composition of binary quadratic forms Appendix. Cycles of stable modules Answers to exercises

Notes:

Includes bibliographical references (pages 207) and index.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Edwards, Harold M. Higher arithmetic :

ISBN:

9781470421533

Access Restriction:

Restricted for use by site license.