# Catalan's conjecture

From Number

## 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 |