Read this problem and would like to share it with all of you.

Given n numbers, a_1, a_2, ..., a_n, each of which is 1 or -1. Assume that
a_1a_2a_3a_4 + a_2a_3a_4a_5 + ... + a_{n-1}a_na_1a_2 + a_na_1a_2a_3 = 0.
Prove that n is a multiple of 4 (i.e., 4 divides n).

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