Problem-solving and selected topics in number theory : in the spirit of the Mathematical Olympiads
This book is designed to introduce some of the most important theorems and results from number theory while testing the reader s understanding through carefully selected Olympiad-caliber problems. These problems and their solutions provide the reader with an opportunity to sharpen their skills and t...
Сохранить в:
| Главный автор: | |
|---|---|
| Формат: | Livre numérique |
| Язык: | Anglais |
| Опубликовано: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Редактирование: | 1st ed. 2011. |
| Предметы: | |
| Online-ссылка: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Примечание: |
Description d'après consultation du 26 avril 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Problem-solving and selected topics in number theory, in the spirit of the mathematical olympiads, Michael Th. Rassias, New-York, Springer, 2011, 1 vol. (XIII-324 p.), 978-1-4419-0494-2 |
Оглавление:
- - Introduction The Fundamental Theorem of Arithmetic Arithmetic functions Perfect numbers, Fermat numbers Basic theory of congruences Quadratic residues and the Law of Quadratic Reciprocity The functions p(x) and li(x) The Riemann zeta function Dirichlet series Partitions of integers Generating functions Solved exercises and problems The harmonic series of prime numbers Lagrange four-square theorem Bertrand postulate An inequality for the function p(n) An elementary proof of the Prime Number Theorem Historical remarks on Fermat s Last Theorem Author index Subject index Bibliography and Cited References