Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads - Softcover
Synopsis
- 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.- Bibliography and Cited References.- Author index.- Subject index.
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