A significant and open conjecture in number theory first made in the 1980s. Given ε‎ > 0, the conjecture says that there are finitely many triples (a,b,c) of coprime positive integers such that a + b = c and c > rad(abc)^{ε‎ + 1}. Here rad(n) denotes the product of the distinct prime factors of n. If true, it would imply other theorems and conjectures including the Mordell conjecture, Catalan’s conjecture, and Fermat’s Last Theorem.