The Beal Conjecture makes the following mathematical statement.
"If [tex]A^{x}+B^{y}=C^{z}[/tex],
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."
"The impossibility of the case A = 1 or B = 1 is implied by Catalan's conjecture, proven in 2002 by Preda Mihăilescu. (Notice C cannot be 1, or one of A and B must be 0, which is not permitted.)"
-- Wikipedia,
https://en.m.wikipedia.org/wiki/Beal_conjecture
Dave,
https://www.researchgate.net/profile/David_Cole29