KöMaL 2006 B3897

For which values of $n$ is it possible to assign values to the variables $x_1,x_2,\ldots,x_n$ from the set {+1,-1} to make the equality $x_1x_2+x_2x_3+x_3x_4+\ldots+x_{n-1}x_n+x_nx_1=0$ true?