# Catalan's conjecture

## Statement

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