Question : Are $$(x,y)=(-2,\pm1),(0,\pm3),(3,\pm6), (6,\pm15),(40,\pm253)$$ the only integer solutions of $\ y^2=x^3+9$ ?
Motivation : I've known that Euler proved that $(x,y)=(3,\pm5)$ are the only integer solutions of $y^2=x^3-2$. This got me interested in the equations $y^2=x^3+k$ where $k$ is an integer. In the $k=9$ case, I can neither find the other solutions nor prove that there is no other solution. Can anyone help?