PMO 2018 Problem 4

Determine all ordered pairs $(x, y)$ of nonnegative integers that satisfy the equation $3x^2 + 2 \cdot 9^y = x(4^{y+1}-1).$

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.