Question 3
Let $n \ge 3$ be a positive integer and let
$$
S = \{k \in \mathbb{N} : (k, n) = (k + 1, n), 1 \le k \le n - 1\}.
$$
Find the remainder of $\prod_{k \in S} k$ divided by $n$.
$$
S = \{k \in \mathbb{N} : (k, n) = (k + 1, n), 1 \le k \le n - 1\}.
$$
Find the remainder of $\prod_{k \in S} k$ divided by $n$.