Find all pairs of integers $(x, y)$ such that $y^3 = 8x^6 + 2x^3 y -y^2$.
Problem
Source: 2017 Saudi Arabia IMO Training Test p7
Tags: number theory, Diophantine equation, diophantine
Source: 2017 Saudi Arabia IMO Training Test p7
Tags: number theory, Diophantine equation, diophantine
Find all pairs of integers $(x, y)$ such that $y^3 = 8x^6 + 2x^3 y -y^2$.