Competitions

USAMO proofs — Proofs

Olympiad statements to prove in full. Write the argument out, then compare it with the model proof — structure, cases and rigor, not just the idea.

Problem 1 of 22
Number theory

Prove that 2\sqrt{2} is irrational.

Write a full proof on paper. There is no answer box — when you are ready, reveal the solution and compare your argument.

Proof practice — USAMO course