The pairs of expression ( ) have interesting characteristics. By (7) and (11), we see the digits in (thus coefficients of ) are placed in reverse order of 's . Since (14) gives us the ratio of to , we can state

For example, in base the equation (14) corresponds to

and

Now I give you a conjecture

Don't you think it's intriguing there are only two integers
9801 and 8712 which satisfy **conjecture 1**?