A number which is simultaneously a nonagonal number 
and heptagonal number 
and therefore satisfies the Diophantine
equation
 |
(1)
|
Completing the square and rearranging gives
 |
(2)
|
Defining 
and 
gives the Pell-like equation
 |
(3)
|
The first integral solutions in 
and 
are 
, (88, 104), (12445, 14725), (1767052, 2090804),
... (OEIS A048919 and A048920),
giving the nonagonal heptagonal numbers 1, 26884, 542041975, 10928650279834, ...
(OEIS A048921).
