KMO 2014 Problem 1

For $x, y$ positive integers, $x^2-4y+1$ is a multiple of $(x-2y)(1-2y)$ . Prove that $|x-2y|$ is a square number.

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.