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AuthorErdล{145}s, Paul. author
TitleTopics in the Theory of Numbers [electronic resource] / by Paul Erdล{145}s, Jรกnos Surรกnyi
ImprintNew York, NY : Springer New York : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4613-0015-1
Descript XVIII, 287 p. online resource

SUMMARY

This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdรถs. Janos Suranyis vast teaching experience successfully complements Paul Erdรถs'ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdรถs was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing problems to the mathematical community which were exquisitely simple to understand yet difficult to solve. He was awarded numerous prestigious prizes including the Frank Nelson Cole prize of the AMS. Professor Janos Suranyi is a leading personality in Hungary, not just within the mathematical community, but also in the planning and conducting of different educational projects which have led to a new secondary school curriculum. His activity has been recognized by, amongst others, the Middle Cross of the Hungarian Decoration and the Erdรถs Award of the World Federation of National Mathematical Competitions


CONTENT

1. Divisibility, the Fundamental Theorem of Number Theory -- 2. Congruences -- 3. Rational and Irrational Numbers. Approximation of Numbers by Rational Numbers (Diophantine Approximation) -- 4. Geometric Methods in Number Theory -- 5. Properties of Prime Numbers -- 6. Sequences of Integers -- 7. Diophantine Problems -- 8. Arithmetic Functions -- Hints to the More Difficult Exercises


Mathematics Number theory Mathematics Number Theory



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