Nonagonal Pentagonal Number
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A048913, A048914, and A048915 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
19-12-2020
1699
Nonagonal Pentagonal Number
A number which is simultaneously a nonagonal number 
and pentagonal number 
and therefore satisfies the Diophantine equation
 |
(1)
|
Completing the square and rearranging gives
 |
(2)
|
Defining 
and 
gives the Pell-like equation
 |
(3)
|
This has solutions in 
corresponding to solutions which are integral in 
and 
of 
, (14, 21), (7189, 10981), (165026, 252081), (86968201, 132846121), ... (OEIS A048913 and A048914), giving the nonagonal pentagonal numbers 1, 651, 180868051, 95317119801, 26472137730696901, ... (OEIS A048915).
REFERENCES:
Sloane, N. J. A. Sequences A048913, A048914, and A048915 in "The On-Line Encyclopedia of Integer Sequences."
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