3-ча 1. Solve the system of equations:

\[
\left\{\begin{aligned}
1-x_{1} x_{2} & =0 \\
1-x_{2} x_{3} & =0 \\
1-x_{3} x_{4} & =0 \\
\cdots & \cdots \\
1-x_{n-1} x_{n} & =0 \\
1-x_{n} x_{1} & =0
\end{aligned}\right.
\]
Solve 1. Answer: \(x_{1}=x_{2}=\cdots=x_{n}= \pm 1\) for odd \(n\), \(x_{1}=x_{3}=\cdots=x_{n-1}=a\) and \(x_{2}=x_{4}=\) \(\cdots=x_{n}=\frac{1}{a}(a \neq 0)\) for even \(n\). For odd \(n\), the solution is essentially provided in the solution to problem 1 for 7th grade. For even \(n\), we similarly obtain \(x_{1}=x_{3}=\cdots=x_{n-1}, x_{2}=x_{4}=\cdots=x_{n-2}\) and \(x_{2}=x_{n}\). It is clear that the sets of unknowns specified in the answer are solutions to the given system of equations.