A Concise Introduction to the Theory of Numbers

Rating:
Summary: Fields Medalist
Review: My copy of this book is worn out. It's hard to explain it's charm, perhaps it's the way it covers so much ground so quickly and fluidly (without leaving everything as an exercise for the reader). A particular emphasis on quadratics: residues, forms, class field - not surprising since the author himself won the Fields Medal for his work binary quadratic forms in 1970 and previously in 1966 proved a long-standing conjecture of Carl Gauss: The only imaginary quadratic fields with unique factorization are d = -1, -2, -3, -7, -11, -19, -43, -67 and -163.

Rating:
Summary: apt title
Review: This book packs in as many concepts as number theory books five times its length (divisibility, arithmetical functions, congruences, quadratic residues and forms and fields, and diophantine equations and approximations) and is still (surprisingly) very clear. There are even exercises to keep you busy.