Let $c = a + b$ be an abc-triple $(a, b, c) \in \mathbb{N}$ with $\text{gcd}(a,b,c) = 1$, with the prime factorizations of $a$ and $b$ known. How can the abc conjecture put constraints on the prime factors of $c$?
I am interested of the 'practical' use of the abc conjecture. I found this nice reddit post: Why would solving the ABC conjecture be of importance to us?, where the commenter explained that even if the factorizations of $a$ and $b$ are known, it is still very difficult to say something about the prime factorization of $c = a + b$. And that the abc conjecture could give constraints on the factors in $c$ in this case, but I don't see how.
I appreciatie references.