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An Introduction to the Theory of Numbers


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Table of Contents

Preface to the sixth editionAndrew Wiles: Preface to the fifth edition 1: The Series of Primes (1) 2: The Series of Primes (2) 3: Farey Series and a Theorem of Minkowski 4: Irrational Numbers 5: Congruences and Residues 6: Fermat's Theorem and its Consequences 7: General Properties of Congruences 8: Congruences to Composite Moduli 9: The Representation of Numbers by Decimals 10: Continued Fractions 11: Approximation of Irrationals by Rationals 12: The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p) 13: Some Diophantine Equations 14: Quadratic Fields (1) 15: Quadratic Fields (2) 16: The Arithmetical Functions o(n), (n), *d(n), *s(n), r(n) 17: Generating Functions of Arithmetical Functions 18: The Order of Magnitude of Arithmetical Functions 19: Partitions 20: The Representation of a Number by Two or Four Squares 21: Representation by Cubes and Higher Powers 22: The Series of Primes (3) 23: Kronecker's Theorem 24: Geometry of Numbers 25: Joseph H. Silverman: Elliptic Curves Appendix List of Books Index of Special Symbols and Words Index of Names General Index

About the Author

Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of Pure Mathematics at Oxford University. He works in analytic number theory, and in particular on its applications to prime numbers and to Diophantine equations.


`Review from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable.' Nature `This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory.' Mathematical Gazette ` important reference work... which is certain to continue its long and successful life...' Mathematical Reviews `...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own.' Matyc Journal

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