Question 83
Let $a$ and $b$ be integers bigger than $2$. Prove that there is a positive integer $k$ and a finite sequence $n_1, n_2, \dots, n_k$ of positive integers, such that $n_1 = a$, $n_k = b$ and $(n_i + n_{i+1}) \mid n_i n_{i+1}$ for every $i = 1, 2, \dots, k-1$.