Again remember what I said. Let be a finite field . Let be an irreducible polynomial over . Then is a field. Now any element in can be written uniquely as now for (for ) we have choices for the coefficients. Thus, in total there are such elements in this larger field.

1)Let

2)Let be an order irreducible polynomial in .

3)The factor ring is a field with elements.

So the thing remaining now is for you to find an irreducible degree polynomial.