A guide to elementary number theory / Underwood Dudley.

Format:

Book

Author/Creator:

Dudley, Underwood, author.

Contributor:

Mathematical Association of America.

Series:

Dolciani mathematical expositions ; no. 41.

MAA guides ; no. 5.

Dolciani Mathematical Expositions, v. 41

Language:

English

Subjects (All):

Number theory.

Physical Description:

1 online resource (x, 141 pages)

Place of Publication:

[Washington, D.C.] : Mathematical Association of America, c2009.

System Details:

Mode of access : World Wide Web

Summary:

"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy."--P. [4] of cover.

Contents:

Introduction Chapter 1. Greatest Common Divisors Chapter 2. Unique Factorization Chapter 3. Linear Diophantine Equations Chapter 4. Congruences Chapter 5. Linear Congruences Chapter 6. The Chinese Remainder Theorem Chapter 7. Fermat's Theorem Chapter 8. Wilson's Theorem Chapter 9. The Number of Divisors of an Integer Chapter 10. The Sum of the Divisors of an Integer Chapter 11. Amicable Numbers Chapter 12. Perfect Numbers Chapter 13. Euler's Theorem and Function Chapter 14. Primitive Roots and Orders Chapter 15. Decimals Chapter 16. Quadratic Congruences Chapter 17. Gauss's Lemma Chapter 18. The Quadratic Reciprocity Theorem Chapter 19. The Jacobi Symbol Chapter 20. Pythagorean Triangles Chapter 21. $x^4+y^4\neq z^4$ Chapter 22. Sums of Two Squares Chapter 23. Sums of Three Squares Chapter 24. Sums of Four Squares Chapter 25. Waring's Problem Chapter 26. Pell's Equation Chapter 27. Continued Fractions Chapter 28. Multigrades Chapter 29. Carmichael Numbers Chapter 30. Sophie Germain Primes Chapter 31. The Group of Multiplicative Functions Chapter 32. Bounds for $\pi (x)$ Chapter 33. The Sum of the Reciprocals of the Primes Chapter 34. The Riemann Hypothesis Chapter 35. The Prime Number Theorem Chapter 36. The abc Conjecture Chapter 37. Factorization and Testing for Primes Chapter 38. Algebraic and Transcendental Numbers Chapter 39. Unsolved Problems

Notes:

Includes index.

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

Description based on print version record.

Other Format:

Print version: Dudley, Underwood. guide to elementary number theory /

ISBN:

9780883859186 (online)

Access Restriction:

Restricted for use by site license.