Hey guys, I was wondering do any of you have any insight into the problem mentioned in the title. Here it is again for good measure:

$\displaystyle x^3 = y^2 + 1$ with $\displaystyle x,y \in \mathbb{N}$

I reckon there's only 1 sol'n, i.e. x = 3 and y = 5

However, despite all my attempts to prove this, nothing seems to work. Any thoughts?