Let n be a positive integer,and let x_1,x_2, \dots ,x_n be numbers that are either 1 or -1. if you know that
x_1x_2+x_2x_3+x_3x_4+\dots+x_{n-1}x_{n}+x_nx_1=0.
Prove that 4\mid n.
Let n be a positive integer,and let x_1,x_2, \dots ,x_n be numbers that are either 1 or -1. if you know that
x_1x_2+x_2x_3+x_3x_4+\dots+x_{n-1}x_{n}+x_nx_1=0.
Prove that 4\mid n.