Question 96
Let $S$ be a set of $n\ge3$ positive integers, none of which is the sum of two other distinct members of $S$. Prove that the elements of $S$ can be ordered as $a_1,a_2,\ldots,a_n$ so that, for every $i=2,3,\ldots,n-1$, $a_i$ divides neither $a_{i-1}+a_{i+1}$ nor $a_{i-1}-a_{i+1}$.