Beal conjecture

Beal's Conjecture is a statement in number theory proposed by Andrew Beal in 1993. It asserts that if \( A^x + B^y = C^z \) holds true for positive integers \( A, B, C, x, y, \) and \( z \) with \( x, y, z > 2 \), then \( A, B, \) and \( C \) must share a common prime factor.