Explicitly check that [7] + [21] = [98] + [-5] in Z13. (b) Suppose that [5] [7] [8] [9] makes sense. Find the value of n if we are working in the 1. ring Zn. 7.5.2 (a) Prove the second half of Theorem 7.18, that is well-defined. 'n (b) Prove by induction that the operation of raising to the power mE N is well-defined in Zn. Le., prove that Vm € N, V[x] €Z we have [x"] = [x]". Be careful! n is fixed, your induction variable is m. What base case(s) do you need?