Question 94
Determine all natural numbers $n$ ($n\gt 1$) with the following property: if $a_{1}, a_{2}, a_{3}, \ldots, a_{k}$ are all the natural numbers less than $n$ and coprime to $n$, ordered as $a_{1}\lt a_{2}\lt a_{3}\lt\cdots\lt a_{k}$, then none of the sums $a_{i}+a_{i+1}$ for $i=1,2, \ldots, k-1$ is divisible by 3.