Divisibility & Congruences
A 22-module path through divisibility & congruences, in study order from foundations to the frontier.
Modules
- Divisibility and the Division Algorithm
- The Greatest Common Divisor
- The Euclidean Algorithm
- Bezout's Identity
- The Extended Euclidean Algorithm
- Euclid's Lemma
- Primes and Composite Numbers
- The Fundamental Theorem of Arithmetic
- gcd and lcm via Prime Factorization
- The Infinitude of Primes
- Elementary Distribution of Primes
- Congruences and Modular Arithmetic
- Residue Classes and Complete Residue Systems
- Modular Inverses
- Linear Congruences
- The Chinese Remainder Theorem
- Fermat's Little Theorem
- Reduced Residue Systems and the Totient Function
- Multiplicativity of the Totient Function
- Euler's Theorem
- Wilson's Theorem
- The Order of an Element and Primitive Roots