Let's assume multiplicative order is infinite. Then [tex]x^k=1, \forall k=1(1)n[/tex]. In the field [tex]F[/tex] the solution of the polynomial [tex]x^k-1=0[/tex] can have at most [tex]k[/tex] distinct solutions. Hence for any [tex]k=1(1)n[/tex] we cannot have infinite roots. And thus the result follows.
