RE: [math-fun] x^n + y^n = z^n + w^n

Of course, Beal's conjecture (for which there is now a prize of U.S.$100,000 for a proof OR a counterexample) goes as follows: BEAL'S CONJECTURE: If A^K +B^L = C^M , where A, B, C, K, L, M are positive integers, and K, L, M are all greater than 2, then A, B, and C must have a common prime factor. Based on recently-discussed equations for which no examples have ever been found, can Beal's conjecture reasonably be extended? In fact, what is the largest such conjecture that's consistent with what's known? --Dan