Ideal for a first course in number theory, this lively, engaging text
requires only a familiarity with elementary algebra and the properties
of real numbers. Author Underwood Dudley, who has written a series of
popular mathematics books, maintains that the best way to learn
mathematics is by solving problems. In keeping with this philosophy, the
text includes nearly 1,000 exercises and problems—some computational
and some classical, many original, and some with complete solutions.The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.
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