Number Theory Topics

Important Notice: The Number Theory section is one of the first sections ever to be developed on Math Online and unfortunately is not up to par with the quality that the rest of the site provides. Regardless, most of the material posted is still readable but be on the look out for many mistakes. The pages in this hub will slowly be reviewed and edited for quality.

1. The Integers, Integer Division, Primes and Composites, and Linear Diophantine Equations

2. Modular Arithmetic, Congruences, Linear Congruences, Fermat's and Wilson's Theorem

3. The d, σ, and ϕ Functions

4. Quadratic Reciprocity

5. Binary Quadratic Forms

6. Arithmetic Functions and Dirichlet Convolutions

7. Approximation and Pell's Equation

7.1. Farey Sequences and Dirichlet's Approximation Theorem
7.2. Irrational Number Approximation
7.3. Algebraic Number Approximation
7.4. Irrational Numbers
7.5. Geometry of Numbers
7.6. Continued Fractions
7.7. Pell's Equation

8. The Prime Number Theorem

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  • 1. Elementary Number Theory (2nd Edition) by Underwood Dudley.
  • 2. An Introduction to the Theory of Numbers (5th Edition) by Ivan Niven.
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