Schinzel's conjecture on the number of equal-sum-and-product solutions

Let $f_1(n)$ denote the number of ordered positive-integer solutions $(x_1,\dots,x_n)$ to

$$x_1+\cdots+x_n=x_1\cdots x_n,$$

for $n\geq 2$.

Schinzel's conjecture.

$$\lim_{n\to\infty} f_1(n)=\infty.$$

The equal sum and product problem asks for a complete description of these solutions and their number. The conjecture remains open, even though explicit families of solutions and bounds for related solution counts are known.