Number Theory

Divisibility & Factors

Prime Numbers

GCD & LCM

Modular Arithmetic

Linear Congruences

Chinese Remainder Theorem

Euler's Totient Function

Fermat's Little Theorem and Euler's Theorem

Jacobi Symbol

Hensel's Lemma and Polynomial Congruences

Primitive Roots

Quadratic Residues and the Legendre Symbol

Quadratic Reciprocity

Diophantine Equations

Orders of Elements and Discrete Logarithms

Pell's Equation

Continued Fractions

Introduction to Primality Testing and Factoring Algorithms

Public-Key Cryptography (RSA and Diffie-Hellman)