Beal conjecture is false as prime factors are not needed for equations with nearness or approximate equality and 28 other counterexamples

Many equations can have Beal like requirements and not have prime factors in common. Beal conjecture raises a question involving x, y, z all greater than 2 as a group. Due to the statement of problem, 3, 3, 2 are greater as a group then 2. Due to that statement of problem, the conjecture is false as many Beal-like equations do not have to have common prime factors.13 + 23   = 32 follows Beal conjecture format without having common prime factors. The conjecture is false by counterexample.