5. Computing primitive roots In this problem you may use two mathematical facts that are demonstrated in the Appendix of this text. First, the proof of Theorem A.20

(p. 268) reveals that if g is a primitive root for Z_p, then it is also a primitive root for Z_p^k, where k is any natural number greater than 2. Second, Theorem A.16 (p. 267)

says that if g is a primitive root for Z_p, then g or g + p is a primitive root for Z_p². Use these facts to compute a primitive root for Z_n^*, where n equals 31920079960009999.