<p/><br></br><p><b> About the Book </b></p></br></br>Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.<br><p/><br></br><p><b> Book Synopsis </b></p></br></br><p>This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given -- making the book self-contained in this respect.<br>The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, <i>p</i>-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of <i>e</i>, to mention a few.<br>Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes -- containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols -- and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.</p>
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