Problem 1

Let n be a positive integer and let a_1, ..., a_k  (k \ge 2) be distinct integers in the set \{ 1, ..., n \} such that n divides a_i(a_{i+1} - 1) for i = 1, ..., k - 1. Prove that n does not divide a_k(a_1 - 1).

Solution

Solution appears elsewhere.