The congruence ABC conjecture for $N$

Let $N$ be an integer. An ABC-solution is a triple $\mathbf{s}=(a,b,c)$ of distinct relatively prime integers satisfying $a+b+c=0$, with $a$ and $b$ negative. For $n>0$, define $\operatorname{rad}(n)$ as the product of all primes dividing $n$, and set

$$f(\mathbf{s},\epsilon)=\log(c)-(1+\epsilon)\log \operatorname{rad}(abc).$$

Congruence ABC conjecture for $N$. For each $\epsilon>0$, there exists a constant $C_\epsilon$ such that

$$f(\mathbf{s},\epsilon)<C_\epsilon$$

for all ABC-solutions $\mathbf{s}$ such that $N\mid abc$. These are weaker, congruence-restricted versions of the ABC conjecture. The source explains that Oesterlé had shown the case $N=16$ implies the full ABC conjecture and proposes the family for every integer $N$; no resolution status is supplied here.