Question 21
Given an integer $n \gt 1$, let $1 = a_1 \lt a_2 \lt \dots \lt a_t = n - 1$ be all the positive integers that are less than $n$ and coprime to $n$. Determine all values of $n$ for which there is no index $i \in \{1, \dots, t-1\}$ satisfying $3 \mid a_i + a_{i+1}$.