NT / Introduction
Introduction to Number Theory
Prime Peaks
Discover structure in divisibility, primes, representations and remainders.
Preparation: Integer arithmetic, prime factorization and fractions.
Current coverage: 12 core stages from Euclid’s algorithm through congruences and coprime counting.
LEVEL 1 · DIFFICULTY 1/5 within this course
Divisibility and Prime Structure
Organize factors and divisors.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 2 · DIFFICULTY 2/5 within this course
Factorials and Representations
Understand place value and repeated factors.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 3 · DIFFICULTY 3/5 within this course
Congruences
Solve problems using remainders.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 4 · DIFFICULTY 4/5 within this course
Integer Equations and Counts
Combine integer constraints with exact counting.
Explore 3 knowledge islands
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →Progress earned through practice
Earn two independent practice stars and one application star, then complete the library skill check for that stage. The check covers the stage’s library prompts, so changing numbers alone is not enough. Hints help you learn; your existing stars and earned rewards stay yours. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.27-university-guides-v2.