Essays in Classical Number Theory

This comprehensive introduction to number theory will reward students and researchers with its insight and thoroughness. Suitable for course use and self-study, it avoids unnecessary abstraction and provides a wealth of thought-provoking examples and problems. The history of the birth of analytic and algebraic number theory is woven throughout.

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Offering a comprehensive introduction to number theory, this is the ideal book both for those who want to learn the subject seriously and independently, or for those already working in number theory who want to deepen their expertise. Readers will be treated to a rich experience, developing the key theoretical ideas while explicitly solving arithmetic problems, with the historical background of analytic and algebraic number theory woven throughout. Topics include methods of solving binomial congruences, a clear account of the quantum factorization of integers, and methods of explicitly representing integers by quadratic forms over integers. In the later parts of the book, the author provides a thorough approach towards composition and genera of quadratic forms, as well as the essentials for detecting bounded gaps between prime numbers that occur infinitely often.