Number Theory Overview

Number theory is a rich and abstract branch of mathematics which explores the fundamental properties of our number system. Whether you're looking for quick practice problems that strengthen your abstract reasoning skills for Olympiad competition topics, or for advanced, open-ended challenges, we have something here for you. The collection of Brilliant problems and articles is large and growing.

Within number theory, you can learn about wide-ranging topics such as:

Brilliant's article collection is expanding to cover every topic you might encounter in any pre-collegiate math program. In most topic areas, we cover the content in much more depth than traditional grade-school standards, with a focus on real understanding instead of memorization.

The most popular introductory Number Theory topics on Brilliant are:

Our goal is to be able to challenge any student in the world with math that stretches their skills. Learning definitions and introductory skills is the first part of mastery in number theory, followed by learning and understanding the theorems and proofs central to this topic.

The most popular pages on Brilliant that prove famous theorems in number theory are:

Whether you're just beginning to study for your first math competition, or if you're a pro aiming for a perfect score, Brilliant is a resource for every trick and topic that you might be looking for. The competitions and exams that Brilliant can help you study for include:

International Math Competitions

• IMO
• IMC
• Mathematical Kangaroo

USA Math Exams and Competitions

• AIME
• AMC8 / AMC10 / AMC12
• AP Exams (AB Calculus, BC Calculus)
• ARML
• MATHCOUNTS
• MOEMS
• SAT
• USAMO
• USAJMO
• USAMTS

Indian Math Exams and Competitions

• RMO
• KVPY
• IIT JEE