I have been interested in the $abc$-conjecture recently, because of its marvelous applications to number theory (e.g., Fermat's last theorem, Mordell-Faltings theorem, etc.).
I've heard of that there is a claimed proof which I'm not sure whether this is true or not. I'm not interested in this one.
But I'd like to see some "right" proof of abc conjecture.
What I mean by right is that even though it does not resolves the problem completely, if it solves some tiny part of the problem, or gives progression on solving the problem, I'll view it as "right".
For example, for the famous Goldbach conjecture, there is fairly noticeable results related to it, called Chen's theorem.
Or for Riemann hypothesis, there is a result asserting that out of the critical strip, there is no nontrivial zeros of Riemann zeta function.
Though those didn't solve the problem completely, I think those give insight to mathematicians and clue to how to solve those problems.
Like above one, if there is any result related to the abc conjecture, I want to read that. If possible, of the most elementary introduction book to that.
Thank you for reading and answering this question.
Edit: I've already read the analogous polynomial version of abc conjecture and what the consequences of abc conjectures and its applications are. I've tried to Mochizuki's paper. But that one was far beyond my knowledge.
