Question 35
We say that a pair $(a, b)$ of positive integers is a *link* if no proper factor of $a + b$ exceeds $\min\{a, b\}$.
Show that for any positive integers $u$ and $v$ there is a positive integer $n$ and a chain $c_0, c_1, \dots, c_n$ of positive integers such that
* $c_0 = u$
* $c_n = v$
* Each pair $(c_{k-1}, c_k)$ for $1 \le k \le n$ is a link.
Show that for any positive integers $u$ and $v$ there is a positive integer $n$ and a chain $c_0, c_1, \dots, c_n$ of positive integers such that
* $c_0 = u$
* $c_n = v$
* Each pair $(c_{k-1}, c_k)$ for $1 \le k \le n$ is a link.