I think that is a good place to start.
Why not take over ?
Give an example of a field and a polynomial which is not the the zero polynomial but for all
I've tried the fields where is prime, but now I don't believe these can work , there are elements in that field, but the highest attainable power is n-2, so that's a dead end, in my understanding.
Fields , , and also don't work, according to my (possibly incorrect) understanding.
Can anyone help out please?