Nguồn ngoài
Elementary Number Theory
The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts.
- Tác giả
- Wissam Raji
- Nhà xuất bản
- American University of Beirut
- Nguồn
- LibreTexts
- Giấy phép
- CC BY
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 49 mục
- 01: Introduction
- 1.01: Algebraic Operations With Integers
- 1.02: The Well Ordering Principle and Mathematical Induction
- 1.03: Divisibility and the Division Algorithm
- 1.04: Representations of Integers in Different Bases
- 1.05: The Greatest Common Divisor
- 1.06: The Euclidean Algorithm
- 1.07: Lame's Theorem
- 02: Prime Numbers
- 2.01: The Sieve of Eratosthenes
- 2.02: The Infinitude of Primes
- 2.03: The Fundamental Theorem of Arithmetic
- 2.04: Least Common Multiple
- 2.05: Linear Diophantine Equations
- 2.06: The function x. the symbols O o and
- 2.07: Theorems and Conjectures involving prime numbers
- 03: Congruences
- 3.01: Introduction to Congruences
- 3.02: Residue Systems and Eulers -Function
- 3.03: Linear Congruences
- 3.04: The Chinese Remainder Theorem
- 3.05: Theorems of Fermat Euler and Wilson
- 04: Multiplicative Number Theoretic Functions
- 4.01: Definitions and Properties
- 4.02: Multiplicative Number Theoretic Functions
- 4.03: The Mobius Function and the Mobius Inversion Formula
- 4.04: Perfect Mersenne and Fermat Numbers
- 05: Primitive Roots and Quadratic Residues
- 5.01: The order of Integers and Primitive Roots
- 5.02: Primitive Roots for Primes
- 5.03: The Existence of Primitive Roots
- 5.04: Introduction to Quadratic Residues and Nonresidues
- 5.05: Legendre Symbol
- 5.06: The Law of Quadratic Reciprocity
- 5.07: Jacobi Symbol
- 06: Introduction to Continued Fractions
- 6.01: Basic Notations
- 6.02: Main Technical Tool
- 6.03: Very Good Approximation
- 6.04: An Application
- 6.05: A Formula of Gauss a Theorem of Kuzmin and Levi and a Problem of Arnold
- 07: Introduction to Analytic Number Theory
- 7.01: Introduct to Analytic Number Theory
- 7.02: Chebyshev's Functions
- 7.03: Getting Closer to the Proof of the Prime Number Theorem
- 08: Other Topics in Number Theory
- 8.01: Cryptography
- 8.02: Elliptic Curves
- 8.03: The Riemann Zeta Function