Question 15
The set $\{S_0\}$ has the single member $(5, 19)$. We derive the set $\{S_{n + 1}\}$ from $\{S_n\}$ by adjoining a pair to $\{S_n\}$. If $\{S_n\}$ contains the pair $(2a, 2b)$, then we may adjoin the pair $(a, b)$. If $\{S\}$ contains the pair $(a, b)$ we may adjoin $(a+1, b+1)$. If $\{S\}$ contains $(a, b)$ and $(b, c)$, then we may adjoin $(a, c)$. Can we obtain $(1, 50)$? $(1, 100)$? If we start with $(a, b)$, with $a \lt b$, instead of $(5, 19)$, for which $n$ can we obtain $(1, n)$?