Description
This course is for students who have a decent understanding of Number Theory and want to master it to succeed on the AIME, especially Problems 10–15, as well as solve early number theory problems on the USAMO, USA(J)MO, or other proof contests. Throughout the course, we will teach many important techniques, tricks, and theorems for solving a variety of number theory problems ranging from easy to hard. We will also cover more obscure topics like Dirichlet convolutions and series that rarely appear on the AIME but do sometimes appear on the HMMT and SMT. Weekly homework will be assigned, and some of the harder problems will be reviewed in class. Additionally, one or two purely number theory mock olympiads around the JMO 1–2 level will be given.
Syllabus
- Number Theory Fundamentals Review
- Diophantine Equations
- Orders
- p-adic Valuations
- Quadratic Residues
- Construction & Existence
- Arithmetic Functions
- Floor and Ceiling Functions
- Miscellaneous
- Full IMO Shortlist N1–N5