FKMO 2007 Problem 3

Find all triples of $(x, y, z)$ of positive intergers satisfying $1+{4}^{x}+{4}^{y}=z^2$ .

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.