JBMO-SL 2014 N3

Find the integer solutions of the equation

$x^{2}=y^{2}\left(x+y^{4}+2 y^{2}\right)$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(x, y)=(0,0), (12,-2), (12,2), (-8,-2), (-8,2)

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.