p^2=p+1.
Since p isn't zero, we may divide through to get p=1+p^-1
Rearranging this, we have p^-1 = p-1
Squaring, we obtain p^-2 = p^2-2p+1, but since p^2=p+1, we simplify this to p^-2 = -p+2. Square again, and then multiply by p^-1, using the equation p^2=p+1 to simplify at each step...