Nonagonal Octagonal Number
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A048922, A048923, and A048924 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
19-12-2020
1395
Nonagonal Octagonal Number
A number which is simultaneously a nonagonal number 
and octagonal 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 
, (425, 459), (286209, 309141), (192904201, 208360351), ... (OEIS A048922 and A048923), giving the nonagonal octagonal numbers 1, 631125, 286703855361, 130242107189808901, ... (OEIS A048924).
REFERENCES:
Sloane, N. J. A. Sequences A048922, A048923, and A048924 in "The On-Line Encyclopedia of Integer Sequences."
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