Hardy G.H., Wright E.M. An Introduction to the Theory of Numbers

Oxford: At the Clarendon Press, 1971. — 421 p.This book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan.
It is not in any sense (as an expert can see by reading the table of contents) a systematic treatise on the theory of numbers. It does not even contain a fully reasoned account of any one side of that many-sided theory, but is an introduction, or a series of introductions, to almost all of these sides in turn. We say something about each of a number of subjects which are not usually combined in a single volume, and about some which are not always regarded as forming part of the theory of numbers at all. Thus Chs. XII-XV belong to the 'algebraic' theory of numbers, Chs. XIX-XXI to the 'additive', and Ch. XXII to the 'analytic' theories; while Chs. Ill, XI, XXIII, and XXIV deal with matters usually classified under the headings of 'geometry of numbers' or 'Diophantine approximation. There is plenty of variety in our programme, but very little depth; it is impossible, in 400 pages, to treat any of these many topics at all profoundly.
There are large gaps in the book which will be noticed at once by any expert. The most conspicuous is the omission of any account of the theory of quadratic forms. This theory has been developed more systematically than any other part of the theory of numbers, and there are good discussions of it in easily accessible books. We had to omit something, and this seemed to us the part of the theory where we had the least to add to existing accounts.
The book is written for mathematicians, but it does not demand anv great mathematical knowledge or technique. In the first eighteen chapters we assume nothing that is not commonly taught in schools, and any intelligent university student should find them comparatively easy reading. The last six are more difficult, and in them we presuppose a little more, but nothing beyond the content of the simpler university courses.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 N k(l), k(i), and k(p)
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
A List of Books
Index of Special Symbols
Index of Names