# Beal conjecture

(Redirected from Beal's conjecture)

The Beal conjecture is a conjecture in number theory. It has also been referred to as the Tijdeman-Zagier conjecture.

If
${\displaystyle A^{x}+B^{y}=C^{z},}$
where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.

Equivalently,

There are no solutions to the above equation in positive integers A, B, C, x, y, z with A, B, and C being pairwise coprime and all of x, y, z being greater than 2.

## References

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