Find alpha_i, in the equations i+x=x^(alpha_i), i=0,1,2,3,4 over the field Z_5[x]/<x^2 + x + 2>.

Show that the sequence of numbers 1, alpha_1, alpha_2, alpha_3, alpha_4 is B_2 sequence with for all i alpha_i< 25.

(all sums alpha_i+alpha_j are distinct)