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Beginning number theory. (English) Zbl 0824.11001

Dubuque, IA: Wm. C. Brown Publishers. xi, 308 p. (1993).
The book is intended for use in an upper-division undergraduate course in elementary number theory. It begins with basic ideas (conjecture, proof, theorem, ordering, methods of proofs, notations and symbols) and then presents a nice building of elementary number theory. The chapters deal with divisibility (greatest common divisor, Euclid’s algorithm, representation of integers); primes (classical results are mentioned whose proofs need in some cases advanced methods); congruences (linear and polynomial congruences, Fermat’s and Wilson’s theorems, primitive roots, quadratic congruences, Legendre and Jacobi symbols); diophantine equations (linear and nonlinear ones, e.g. Pythagorean, Pell’s and Mordell’s equations); arithmetic functions (sigma, tau and Euler’s functions, Dirichlet product, Möbius transformation, perfect numbers); continued fractions (finite and infinite ones and their application in diophantine approximation).
Interesting chapters are those which present the elements of computational number theory, cryptology and the basic properties of linear recurrences; these are missing in general from introductory works. Many numerical examples, exercises for the readers, open questions and historical comments complete the book.
Reviewer: P.Kiss (Eger)

MSC:

11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11Axx Elementary number theory
11Dxx Diophantine equations
11Yxx Computational number theory
11B37 Recurrences
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