Vô Conjecture 20 series 1 (VC20S1)

We study integer solutions to the exponential Diophantine equation a^x+b^y=c^z\bigm under the constraints that the exponents are pairwise distinct and greater than 2. We propose a conjectural structural property asserting that among the bases a,b,c, at least one pair satisfies a divisibility relation. As a consequence, the conjecture implies a nontrivial instance of the Beal-type phenomenon concerning common prime divisors.