Problem-Solving and Selected Topics in Number Theory In the Spirit of the Mathematical Olympiads /

• Κύριος συγγραφέας: Rassias, Michael Th (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2011.
• Θέματα: Mathematics.; Number theory.; Number Theory.

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...

Πίνακας περιεχομένων:

• - 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.