Comment by chaoxu

I think it would work for all finite fields. One of the solutions to this IOI problem was solved that way, and it's not of the form GF(p) but it's GF(p^2). http://olympiads.win.tue.nl/ioi/ioi94/contest/day2prb1/probl... see solution 2: http://olympiads.win.tue.nl/ioi/ioi94/contest/day2prb1/solut...