CZ-SK-MO 1983 Problem 5

Find all pair $(x,y)$ of positive integers satisfying $\left|\frac{x}{y}-\sqrt2\right|<\frac{1}{y^3}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.