一个同时是七边形数 
和六边形数 
的数。 这样的数在以下情况下存在
 |
(1)
|
配方法和重新排列得到
 |
(2)
|
Substituting 
and 
gives the Pell-like quadratic Diophantine equation
 |
(3)
|
which has solutions 
, (7, 3), (18, 8), (47, 21), (123, 55), .... The integer solutions in 
and 
are then given by 
, (221, 247), (71065, 79453), (22882613, 25583539), ... (OEIS A048902 and A048901), corresponding to the heptagonal hexagonal numbers 1, 121771, 12625478965, 1309034909945503, ... (OEIS A048903).
