Beal conjecture

History

This conjecture was made by Andrew Beal, a mathematics hobbyist, while investigating Fermat's last theorem.

Statement

Consider the equation:

.

The Beal conjecture (also called Beal's conjecture) states the following equivalent things:

1. This equation has no solutions for  pairwise relatively prime positive integers, and  all natural numbers greater than .
2. This equation has no solutions for  pairwise relatively prime integers (all nonzero) and  all natural numbers greater than .

Related facts

Weaker facts and conjectures

• Fermat's last theorem: This is the special case . This was conjectured by Fermat and proved by Wiles, building on work by several mathematicians in between.