p^3(p^2+1)=(q-2)(q+1) +)Case 1:p=3 +)Case 2:p isn't 3. Assume p divides both q-2 and q+1 Then (q+1)-(q-2)=3 is divisible by p (Contraction) This means p can't divide both q-2, q+1 -> Either q+1 or q-2 is divisble by p^3. Do a small demonstration if q+1 is divisble by p^3 q+1>=p^3. Follows q-2<=p^2+1 -> p^3<=q+1<=p^2+3 (Contraction)