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Each of the numbers $x_1, x_2,\dots, x_n, n > 4,$ is equal to $1$ or $–1.$ Suppose, $x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + \dots + x_{n–3}x_{n–2}x_{n–1}x_n + x_{n–2}x_{n–1}x_nx_1+ x_{n–1}x_nx_1x_2 + x_nx_1x_2x_3= 0$, then,

  1. $n$ is even.
  2. $n$ is odd.
  3. $n$ is an odd multiple of $3.$
  4. $n$ is prime

 

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