An introduction to the theory of numbers/ G.H. Hardy and E.M. Wright

Includes bibliography and index

The Series of Primes (1) -- The Series of Primes (2) -- Farey Series and a Theorem of Minkowski -- Irrational Numbers -- Congruences and Residues -- Fermat’s Theorem and its Consequences -- General Properties of Congruences -- Congruences to Composite Moduli -- The Representation of Numbers by Decimals -- Continued Fractions -- Approximation of Irrationals by Rationals -- The Fundamental Theorem of Arithmetic -- Some Diophantine Equations -- Quadratic Fields (1) -- Quadratic Fields (2) -- The Arithmetical Functions φ(n), μ(n), d(n), σ(n), r(n) -- Generating Functions of Arithmetical Functions -- The Order of Magnitude of Arithmetical Functions -- Partitions -- The Representation of a Number by Two or Four Squares -- Representation by Cubes and Higher Powers -- The Series of Primes (3) -- Kronecker’s Theorem -- Geometry of Numbers -- Elliptic Curves

An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory — modular elliptic curves and their role in the proof of Fermat's Last Theorem — a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.