Number theory is a broad topic, and may cover many diverse subtopics, such as:
Some branches of number theory may only deal with a certain subset of the real numbers, such as integers, positive numbers, natural numbers, rational numbers, etc. Some algebraic topics such as Diophantine equations as well as some theorems concerning integer manipulation (like the Chicken McNugget Theorem ) are sometimes considered number theory.
Student Guides to Number Theory
- Introductory topics in number theory
- Intermediate topics in number theory
- Olympiad topics in number theory
- Advanced topics in number theory
- General Interest
Other Topics of Interest
These are other topics that aren't particularly important for competitions and problem solving, but are good to know.