Catalan's conjecture

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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