Fermat proved that $x^3-y^2=2$ has only one solution $(x,y)=(3,5)$. After some search,i found only proofs using factorization over the ring $Z[\sqrt{-2}]$. My question is: Is this Fermat's original proof?If not where can i find it? Thank you for viewing Note: I am not expecting to find Fermat's handwritings because this may not exist. I was hoping to find a proof that would look more ''Fermatian''