[ Systems of nonlinear algebraic equations ]

Given the system of equations:

$$
\left\{\begin{aligned}
& x_{1} x_{2} \cdot \ldots \cdot x_{1962}=1 \\
& x_{1}-x_{2} x_{3} \cdot \cdots \cdot x_{1962}=1 \\
& x_{1} x_{2}-x_{3} x_{4} \cdot \cdots \cdot x_{1962}=1 \\
& \cdots \cdots \cdots \cdots \cdots \\
& x_{1} x_{2} \cdot \ldots \cdot x_{1961}-x_{1962}=1
\end{aligned}\right.
$$

What values can $x_{25}$ take?

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