DE-BUNDESWETTBEWERB 2009 Problem 1

Determine all possible digits $z$ for which $\underbrace{9...9}_{100}z\underbrace{0...0}_{100}9$ 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.