Mod Arith 1: Proofs
One of two beginner units in number theory focusing on modular arithmetic. Emphasis on basic proof-based problems, starting with simple Diophantine equations that can be solved by taking moduluses and factoring. The two Modular Arithmetic units can be done in either order.
This unit gives a general introduction to modular arithmetic in olympiad number theory.
It's considered a more accessible B-unit, requiring very little reading and has a friendly problem set.
The problems in this unit come in two types:
- Diophantine Equations: General practice with lots of diophantine equations where the solution usually involves taking the correct mod.
- General mod problems: Similar to entry combo, gives you some easier problems that use modular arithmetic. Combinatorial ideas apply as well.
Notable problems
- PEN H61: extremely generic, well-known, frequently asked diophantine equation.
- JMO 2012/5: Classic mod problem that uses some combinatorial intuition.