abc conjecture

For any ε > 0, there are only finitely many triples (a,b,c) of coprime positive integers with a + b = c such that c > rad(abc)^(1+ε), where rad denotes the squarefree radical.

The conjecture has profound consequences in number theory. Shinichi Mochizuki's inter-universal Teichmüller theory claims to prove it, but the proof has not gained general acceptance among experts.