Browkin–Brzeziński's n-terms abc conjecture

Let $n\ge3$. For integers $x_1,\ldots,x_n$, write $\operatorname{rad}(x_1x_2\cdots x_n)$ for the largest positive squarefree divisor of their product. The n-terms abc conjecture. There is a number $M_n$ depending only on $n$ such that, given integers $x_1,\ldots,x_n$ satisfying

$$\gcd(x_1,\ldots,x_n)=1,\qquad x_1+\cdots+x_n=0,$$

and such that no proper subsum in the second relation vanishes, one has

$$\max_{1\le j\le n}|x_j|\le \operatorname{rad}(x_1x_2\cdots x_n)^{M_n}.$$

Browkin and Brzeziński proposed this extension of the abc conjecture to $n$ terms. The source also records the sharper expected choice $M_n=2n-5+\epsilon$ for every $\epsilon>0$, up to finitely many exceptions; no resolution status is supplied.