@JaredSummers My intuition told me to pick right hand values that are relatively prime.

Does that have any relevance or did I just get lucky.

In your example 4 and 6 share a common factor, 2, and so that gets rejected.

The pairs \\( 2|4 , 5|15 \rightarrow 2 + 5 | 4 + 15 = 7 | 19 \\) seems to support the intuition

as does \\( 2|4 , 3|3 \rightarrow 2+3 | 4+3 = 5|7 \\).

Does that have any relevance or did I just get lucky.

In your example 4 and 6 share a common factor, 2, and so that gets rejected.

The pairs \\( 2|4 , 5|15 \rightarrow 2 + 5 | 4 + 15 = 7 | 19 \\) seems to support the intuition

as does \\( 2|4 , 3|3 \rightarrow 2+3 | 4+3 = 5|7 \\).