Please solve this problem and explain how you solved it step by step in detail. See illustrations of Lemma 6 and Lemma 8 which are shown at the end of this problem.

6. Let n 1427. (a) Compute and tabulate 51 mod n for i = 1, 2, , n-1. Observe the result is a permutation of (1,2, ,n - 1), as proved by Lemma 6. (b) Compute and tabulate 6i mod n for i- 1,2, . , n-1. Explain why the result is not a permutation of (1,2, ,n -1). (c) Let Zi4 be set of positive integers smaller than 14 and prime relative to 14. 14, 14. Observe that every row is a permutation of Zi4, as proved by Lemma 8