No complete proof or counterexample has been found since Andrew Beal proposed the conjecture in 1993. Partial results confirm it for many specific combinations of exponents, but a general argument covering every combination, or a single counterexample disproving it, has eluded both professional and amateur attempts despite the million dollar prize Beal has offered.
What would resolve this A general proof covering every valid combination of A, B, C, x, y and z, or a single confirmed counterexample: one solution where A, B and C share no common prime factor.
OpenNumber theoryBeal Conjecture (Wikipedia)