The weak form of Szpiro's conjecture

For a non-zero integer $a$, let $N(a)$ be its algebraic radical:

$$N(a)=\prod_{p\mid a}p.$$

Weak form of Szpiro's conjecture. There exists a constant $s>0$ such that, for mutually coprime integers $A$, $B$, and $C$ satisfying $A+B=C$,

$$|ABC|<N(ABC)^s.$$

This conjecture is used to prove finiteness results for Diophantine equations involving products of divisible sequences, generalizing a result concerning $n!+A=x^2$. Its status is unresolved.