Nonagonal Heptagonal Number
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A048919, A048920, and A048921 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
18-12-2020
1397
Nonagonal Heptagonal Number
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).
REFERENCES:
Sloane, N. J. A. Sequences A048919, A048920, and A048921 in "The On-Line Encyclopedia of Integer Sequences."
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