Consider n numbers x1, x2, . . . , xn laid out on a circle andsome value ?. Consider the requirement that every number equals ?times the sum of its two neighbors. For example, if ? were zero,this would force all the numbers to be zero. (a) Show that, nomatter what ? is, the system has a solution. (b) Show that if ? = 12 , then the system has a nontrivial solution. (c) Show that if ? =? 1 2 , then there is a nontrivial solution if and only if n iseven.
