Consider the even number $ 128 = $ 2 ^ 7 that would satisfy the ABC-Conjecture requirements according to the two distinct examples below:

- $ (1) $ $ 3 + 5 ^ 3 = $ 2 ^ 7
- $ (2) $ $ 31 + 97 = $ 2 ^ 7

But in $ (1) $, $ rad (abc) <c $ in $ (2) $, $ rad (abc)> c $. (Note that $ 128 is an even number which is not a counterexample of Goldbach's conjecture, and there is always an infinite number of such non-counterexamples).

It seems then **in general**, if we **only** know that $ c $ is same and that it exists $ a $ and $ b $ such as $ (a, b, c) $ would form an ABC-Conjecture triplet, then it would be impossible so invalid to claim $ rad (abc) <c $, or $ rad (abc)> c $.

Would it be true?