An Introduction to the Theory of NumbersAn 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. HeathBrown, 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 endofchapter 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. Roger HeathBrown 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. Preface to the sixth edition Andrew 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 ø(n), m(n), d(n), σ(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. Elliptic Curves, Joseph H. Silverman Appendix List of Books Index of Special Symbols and Words Index of Names General Index 
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