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# Higher Arithmetic: An Algorithmic Introduction to Number Theory

### About this Title

**Harold M. Edwards**, *New York University, New York, NY*

Publication: The Student Mathematical Library

Publication Year
2008: Volume 45

ISBNs: 978-0-8218-4439-7 (print); 978-1-4704-2153-3 (online)

DOI: http://dx.doi.org/10.1090/stml/045

MathSciNet review: MR2392541

MSC: Primary 11-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- 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