I need a little help im close but stuck.
1. Is there a field with 25 elements?
Well I know that |V_F|=p^n, where p is a prime. Then |V_F|=p^n=25=5^2, p=5, n=2. So now I have to construct the monic irreducible polynomial I know that it is degree 2 but how do you get the correct coefficients? I think the field is related to Z_5/p(x). but im stuck.
2. If W_F has 49 element, the what are the possibilities for F. Describe the collection of subspaces of W_F for each case.
thanks for the help.