Question 22
Let every one of the numbers $x_1$, $x_2$, ..., $x_n$ be equal to $1$ or $-1$ and also:
$$
x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + ... + x_{n-2}x_{n-1}x_nx_1 + x_{n-1}x_nx_1x_2 + x_nx_1x_2x_3 = 0
$$
Prove that $n$ is divisible by $4$.
$$
x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + ... + x_{n-2}x_{n-1}x_nx_1 + x_{n-1}x_nx_1x_2 + x_nx_1x_2x_3 = 0
$$
Prove that $n$ is divisible by $4$.