Number Theory
Overview
Section titled “Overview”Number theory problems are often about finding the right modulus, controlling divisibility, or trapping integer solutions with size and parity constraints.
Checklist
Section titled “Checklist”- Check parity and small moduli first.
- Factor expressions before applying congruences.
- Track valuations when prime powers matter.
- Bound variables when an equation mixes growth rates.
- Search for descent if a smallest solution leads to a smaller one.
Common moves
Section titled “Common moves”- Work modulo a carefully chosen prime or prime power.
- Use gcd facts to split divisibility.
- Apply Fermat, Euler, Wilson, or CRT when the structure calls for it.
- Prove impossibility by infinite descent or contradiction modulo a base.
Practice problems
Tags: number-theory
| Done | Problem | Source | Difficulty | Tags |
|---|---|---|---|---|
| Putnam 2023 A1 | Putnam | 3 | combinatorics, number-theory | |
| Starter Number Theory Problem | Boilerplate | 3 | number-theory, divisibility |