Citation
Mohamat Johari, Mohamat Aidil and Mohd Atan, Kamel Ariffin and Sapar, Siti Hasana
(2014)
Relation between sum of 2mth powers and polynomials of triangular numbers.
JP Journal of Algebra, Number Theory and Applications, 34 (2).
pp. 109-119.
ISSN 0972-5555
Abstract
Let Ф (m, k)(n) denote the number of representations of an integer n as a sum of k 2mth powers and Ψ (m, k)(n) denote the number of representations of an integer n as a sum of k polynomial Pm(γ), where γ is a triangular number. We show that Ф (2, k)(8n + k) = 2k Ψ(2,k) (n) for 1 ≤ k ≤ 7. A general relation between the number of representations (formula presented) and the sum of its associated polynomial of triangular numbers for any degree m ≥ 2 is given as Ф(m, k) (8n + k) = 2k Ψ (m, k) (n).
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Institute for Mathematical Research |
| Publisher: | Pushpa Publishing House |
| Keywords: | Number of representations; Polynomial; Triangular numbers |
| Depositing User: | Nurul Ainie Mokhtar |
| Date Deposited: | 11 Oct 2016 02:47 |
| Last Modified: | 11 Oct 2016 02:47 |
| URI: | http://psasir.upm.edu.my/id/eprint/35199 |
| Statistic Details: | View Download Statistic |
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