This book is a genetic introduciton to algebraic number theory which follows the development of the subject in the work of Fermat, Kummer and others, motivating new ideas and techniques by explaining the problems which led to their creation. The central problem is the one indicated in the title, but many other basic questions of algebraic number thoery are also treated.

Autorentext

Harold M. Edwards [1936-2020] was Professor Emeritus of Mathematics at New York University. His research interests lay in number theory, algebra, and the history and philosophy of mathematics. He authored numerous books, including Riemann's Zeta Function (1974, 2001) and Fermat's Last Theorem (1977), for which he received the Leroy P. Steele Prize for mathematical exposition in 1980. David A. Cox (Contributing Author) is Professor Emeritus of Mathematics in the Department of Mathematics and Statistics of Amherst College. He received the Leroy P. Steele Prize for mathematical exposition in 2016 for his book Ideals, Varieties, and Algorithms, with John Little and Donal O'Shea.

Inhalt
1 Fermat.- 2 Euler.- 3 From Euler to Kummer.- 4 Kummer's theory of ideal factors.- 5 Fermat's Last Theorem for regular primes.- 6 Determination of the class number.- 7 Divisor theory for quadratic integers.- 8 Gauss's theory of binary quadratic forms.- 9 Dirichlet's class number formula.- Appendix: The natural numbers.- Answers to exercises.