Catalan's conjecture

Statement

This conjecture states that the solution set to Catalan's Diophantine problem:

$x^{p}-y^{q}=1$,

for $x,y\neq 0,1$ and $p,q$ positive integers greater than one, has precisely one solution: $x=3,y=2,p=2,q=3$.

The conjecture has been proved.