Number Theory· Study notes
Discrete and Data
The integers from the ground up: divisibility, primes, gcd and the Euclidean algorithm, modular arithmetic, bases, Diophantine equations, Fermat and Euler, arithmetic functions, the Chinese remainder theorem, and orders.
What you'll be able to do
- Prove divisibility facts from definitions
- Compute with congruences, inverses and big powers
- Solve linear and factorable Diophantine equations
- Use Fermat, Euler, CRT and orders on contest problems
Read the notes as a guided lesson
Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics
Primes and Factorization
4 lessonsThe atoms of arithmetic and the unique way numbers split into them
GCD, LCM and the Euclidean Algorithm
5 lessonsGreatest common divisors, Bézout, and fast computation
Modular Arithmetic
4 lessonsCongruences, inverses and linear congruences
Digits and Bases
4 lessonsPlace value in any base and the tricks it enables
Diophantine Equations
4 lessonsInteger solutions: linear equations, factoring tricks and bounding
Fermat, Euler and Wilson
4 lessonsThe three theorems behind every big power
Arithmetic Functions
4 lessonsCounting and summing divisors, and multiplicativity
The Chinese Remainder Theorem
4 lessonsSolving systems of congruences
Orders and Primitive Roots
4 lessonsHow powers cycle, and quadratic residues
Hard Number Theory
4 lessonsContest-level problems that combine everything