# ABC Conjecture

An exciting story has developed over the past few months. In August 2012, after months of rumors, the mathematician Shinichi Mochizuki rounded out a series of papers which he claims prove the ABC Conjecture:

For every ε > 0, there are only finitely many triples of coprime positive integers a + b = c such that c > d^(1+ε), where d denotes the product of the distinct prime factors of abc.

This easy to state conjecture has many important consequences in number theory. Professor Mochizuki has garnered an abundance of coverage from the popular media in the ensuing months due to the novelty of his approach; it is unclear (assuming correctness) how long it would take for his proof to be accepted by the mathematical community.