This conjecture states that the solution set to Catalan's Diophantine problem:
for positive integers not equal to and positive integers greater than one, has precisely one solution: .
The conjecture has been proved.
Relation with other facts/conjectures
|Conjecture||Statement of conjecture||Status|
|Fermat-Catalan conjecture||has only finitely many solutions for positive integers and||open|
|abc conjecture||For every , there exists such that if , then , the product over prime|