ÖMO 2010 Problem 2

Determine all triples $(x, y, z)$ of positive integers $x > y > z > 0$ , such that $x^2 = y \cdot 2^z + 1$

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.