RU-ALLRUSSIAN 1978 Problem 9

The set $\mathrm{S_0}$ has the single member (5, 19). We derive the set $\mathrm{S_{n + 1}}$ from $\mathrm{S_n}$ by adjoining a pair to $\mathrm{S_n}$ . If $\mathrm{S_n}$ contains the pair (2a, 2b), then we may adjoin the pair (a, b). If $\mathrm{S}$ contains the pair (a, b) we may adjoin (a+1, b+1). If $\mathrm{S}$ 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 < b, instead of (5, 19), for which n can we obtain (1, n)?