R = PolynomialRing(GF(5),['x']); R.inject_variables() 
P=x^3 + 2*x + 4
Q=x^3 + x^2 + 1
for i in [0..4]:
     print P(i)
for i in [0..4]:
     print Q(i)
for a2 in [0..4]:
     for a1 in [0..4]:
         for a0 in [0..4]:
             if (P(a2*x^2+a1*x+a0) % Q) == 0:
                 print(a2*x^2+a1*x+a0)
x^31 % P
for a2 in [0..4]:
     for a1 in [0..4]:
         for a0 in [0..4]:
             if ((a2*x^2+a1*x+a0)^4 % Q) == 1:
                 print(a2*x^2+a1*x+a0)