Catalan's conjecture

Statement

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

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

for $x,y$ positive integers not equal to $0,1$ 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.