Question 390908
Hmm.  Look at http://en.wikipedia.org/wiki/Primitive_element_%28finite_field%29.  You must be a math major in 2nd, 3rd year college?  Or a college math professor?  Ha ha.  There are some excellent books in abstract algebra/Galois theory you can look at, like Gallian, Fraleigh, Hungerford, Artin, to name a few.