Skip to main content
\(\newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)
MATH3170:
Number Theory
Contents
Prev
Up
Next
Contents
Prev
Up
Next
1
Introduction
Sets of Numbers
The Diophantine equation
\(a^2+b^2=c^2\)
Induction
2
Divisibility
Division Algorithm
Euclidean Algorithm
Linear Diophantine equations
3
Primes
The Fundamental Theorem of Arithmetic
Number of Primes
Chebychev's Functions
Chebychev's Theorem
4
Congruences
Solving Linear Congruences
Chinese Remainder Theorem
Polynomial Congruences
Polynomials
Fermat Numbers
Mersenne Primes
5
Primality
Sieve of Eratosthenes
Factoring Integers
A more general Sieve
Some Contributions of Fermat
Pseudoprimes and Carmichael Numbers
Wilson's Theorem
6
Number Theoretic Functions
Euler's
\(\varphi\)
-function
The
\(d\)
- and
\(\sigma\)
-functions
Sums over divisors
The Möbius Function
A Completely Multiplicative Function
Möbius Inversion
Patterns in
\(\{\mu(n)\}_n\)
7
Order of Elements of
\(\mathbb{Z}_n\)
Primitive Roots
Applications of Primitive Roots
8
Some Base Results
9
Quadratic Residues
Legendre's Symbol
Gauss' Lemma
The Floor Function
An Important Lemma
Quadratic Reciprocity
10
The Fibonacci Sequence
Divisibility properties
Some identities
11
Continued Fractions
Finite Continued Fractions
Convergents
Linear Diophantine equations
More properties of convergents
A
Special Divisibility Tests
Authored in PreTeXt
Chapter
2
Divisibility
2.1
Division Algorithm
2.2
Euclidean Algorithm
2.3
Linear Diophantine equations