DANUBE 2019 Problem 1

Solve in $\mathbb{Z}^2$ the equation: $x^2\left( 1+x^2 \right) =-1+21^y.$ Lucian Petrescu

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.