Freud R., Gyarmati E. Number Theory

American Mathematical Society, 2021. — 563 p. — (Pure and Applied Undergraduate Texts 48). — ISBN 9781470456917.Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.Basic Notions
Congruences
Congruences of Higher Degree
Legendre and Jacobi Symbols
Prime Numbers
Arithmetic Functions
Diophantine Equations
Diophantine Approximation
Algebraic and Transcendental Numbers
Algebraic Number Fields
Ideals
Combinatorial Number TheoryAnswers and Hints
Historical Notes