I am asked to prove:
I was sick during the week where my proffesor went over this and I cannot understand his notes.
My current approach is to find the roots over the normal polynomial (in this case 4 and 5) and look for the elements that can be generated with their powers (i.e $4^2 = 16 \equiv_6 4$, $4^3=64 \equiv_6 4$, $5^2 = 25 \equiv_6 1$, $5^3 = 125 \equiv_6 5$)...
And try to find some general pattern. However (1-5=-4 $\equiv_6 2$) is not a root. So it seems I am completely off.