Overview

USAMO solutions are written proofs. This module focuses on clarity, structure, and logically complete arguments.

Key Ideas

• State what you are proving and define all variables.
• Use complete sentences and justify each step.
• Highlight the key invariant or construction early.

Worked Example

To prove a statement for all integers $n\ge1$, write a base case and then an inductive step or a direct argument that covers all cases.

Practice Problems