Oesterlé-Masser Conjecture/Formulation 1

Theorem
Let $\epsilon \in \R$ be a strictly positive real number.

There exists only a finite number of triples of (strictly) positive integers $\tuple {a, b, c}$ with the conditions:
 * $a + b = c$
 * $a$, $b$ and $c$ are pairwise coprime

such that:


 * $c > \map {\operatorname {rad} } {a b c}^{1 + \epsilon}$

where $\operatorname {rad}$ denotes the radical of an integer.

Also see

 * Equivalence of Definitions of Oesterlé-Masser Conjecture