Parity Condition on Sequence of 1 and -1

Question

Each of the numbers $x_1, x_2, \dots, x_n$ ($n \ge 4$) is equal to $1$ or $-1$. Suppose $$x_1 x_2 x_3 x_4 + x_2 x_3 x_4 x_5 + \dots + x_n x_1 x_2 x_3 = 0$$ then:

Accepted Answer

A. There are $n$ terms in the sum, each being $+1$ or $-1$. For the total sum to be $0$, there must be an equal number of $+1$s and $-1$s. Therefore, $n$ must be even (and in fact a multiple of 4).

Answer

$n$ is even

Answer

$n$ is odd

Answer

$n$ is an odd multiple of 3

Answer

$n$ is prime

Parity Condition on Sequence of 1 and -1

Explanation

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