Question 162
Prove that for every $n \geq 2$ we can find $n$ real numbers $x_{1}, x_{2}, \cdots, x_{n} \neq 1$ such that the products
$$
x_{1} \cdot x_{2} \cdot \ldots \cdot x_{n} \quad \text{ and } \quad \frac{1}{1-x_{1}} \cdot \frac{1}{1-x_{2}} \cdot \ldots \cdot \frac{1}{1-x_{n}}
$$
are equal.
$$
x_{1} \cdot x_{2} \cdot \ldots \cdot x_{n} \quad \text{ and } \quad \frac{1}{1-x_{1}} \cdot \frac{1}{1-x_{2}} \cdot \ldots \cdot \frac{1}{1-x_{n}}
$$
are equal.