Concise Reason (t) If F is a field with 32 elements, and x is a non-zero and non-identity element of F, then what are the possibilities for the smallest positive integer n with x" = 1? Concise Reason u) Let R = Z[x] be the ring of polynomials in x with integer coefficients. Then does the subgroup generated by the polynomial p(x) = x + 1 in the abelian group (R, +) (which in group theory, we would denote by (x + 1)) have the same elements as the ideal generated by p(x) = x + 1 in the commutative ring (R,+,) (which in ring theory, we would denote by (x + 1))? Concise Reason Have a good summer!