hence where are finite fields. if we're done. so suppose that since is odd, must be odd for all consider two cases:
case 1: for some without loss of generality we assume that choose and let then is clearly a non-invertible element
of but because contradiction!
case 2: if then which is impossible because the problem assumes that therefore now let then is a
non-invertible element of and which is again a contradiction! Q.E.D.