TITLE: diophantine equations $x^3-2y^3=1$
QUESTION [8 upvotes]: I'm not familiar with diophantine equations. At most my approaches doesn't give results. I need to solve the following equation
$$x^3-2y^3=1$$
Where $x,y,z\in\mathbb{Z}$
I know $x=-1,y=-1.x=1,y=0,$ Aware of any other integer solutions. Prove

REPLY [7 votes]: You have found the only solutions. These things are not so easy to prove. This one is done in Mordell's book, Diophantine Equations, in Chapter 15.