Hello

Consider the two finite fields and and let n be a prime number, q be a generator of .

Now show that the polynomial is irreducible over -->

Well if I define then I think I'll have to assume that f(X)=h(X)*g(X) over with degree(h)>0 and degree(g)>0 ? But how does one do that?

q has order n-1. What does that mean? Doesn't that mean that f(q) has order n-1 as well? How can I prove this?