Nathanson Additive Number Theory: Inverse Problems And The Geometry of Sumsets

Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the …

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods.