id: 06351544
dt: b
an: 2015f.00614
au: Kraft, James S.; Washington, Lawrence C.
ti: Elementary number theory.
so: Textbooks in Mathematics. Boca Raton, FL: CRC Press (ISBN
978-1-4987-0268-3/hbk). xvi, 393~p. (2015).
py: 2015
pu: Boca Raton, FL: CRC Press
la: EN
cc: F65
ut: linear Diophantine equations; unique factorization; Congruences; Fermat;
Euler; Wilson; cryptography; primitive roots; quadratic reciprocity;
sums of squares; arithmetic functions; continued fractions
ci:
li:
ab: This is a nice introduction to elementary number theory, designed for use
in a basic undergraduate course. It can be used also for advanced high
school students taking an accessible approach for an independent study.
The book underlines the role of number theory in pure mathematics and
its applications to cryptography and other areas. The first chapter,
entitled Divisibility, includes a section on how to do proofs and a
brief discussion of lemmas, propositions, theorems, and corollaries.
The other chapters are: 2. Linear Diophantine equations, 3. Unique
factorization, 4. Applications of unique factorization, 5. Congruences,
6. Fermat, Euler, Wilson, 7. Cryptographic applications, 8. Order and
primitive roots, 9. More cryptographic applications, 10. Quadratic
reciprocity, 11. Primality and factorization, 12. Sums of squares, 13.
Arithmetic functions, 14. Continued fractions, 15. Recent developments.
The book offers many pedagogical features. The “check your
understanding” problems scattered throughout the chapters assess
whether students have learned certain essential information. At the end
of every chapter, exercises reinforce an understanding of the material.
Other exercises introduce new and interesting ideas while computer
exercises reflect the kinds of explorations that number theorists often
carry out in their research. Appendix A includes supplementary topics,
while Appendix B contains answers and hints of odd-numbered exercises.
rv: László Tóth (Pécs)