Problem-Solving and Selected Topics in Number Theory : In the Spirit of the Mathematical Olympiads （2011）

Rassias, Michael Th.

Springer-Verlag New York Inc.（2014/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 324 p.
• 言語 ENG
• 商品コード 9781489981943
• DDC分類 512

Full Description

The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

Contents

- 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.