Beal conjecture

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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.

Other related facts

Failure of slight modifications of the conjecture

External links