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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rassias, Michael Th (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Temas:
Number theory.
Number Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • - 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.

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