Relation between sum of 2mth powers and polynomials of triangular numbers
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 r...
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| Format: | Article |
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Pushpa Publishing House
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/35199/ http://psasir.upm.edu.my/id/eprint/35199/1/Relation%20between%20sum%20of%202mth%20powers%20and%20polynomials%20of%20triangular%20numbers.pdf |
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| author | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana |
| author_facet | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana |
| author_sort | Mohamat Johari, Mohamat Aidil |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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). |
| first_indexed | 2025-11-15T09:27:20Z |
| format | Article |
| id | upm-35199 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:27:20Z |
| publishDate | 2014 |
| publisher | Pushpa Publishing House |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-351992016-10-11T02:47:33Z http://psasir.upm.edu.my/id/eprint/35199/ Relation between sum of 2mth powers and polynomials of triangular numbers Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana 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). Pushpa Publishing House 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/35199/1/Relation%20between%20sum%20of%202mth%20powers%20and%20polynomials%20of%20triangular%20numbers.pdf 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 http://www.pphmj.com/abstract/8678.htm |
| spellingShingle | Mohamat Johari, Mohamat Aidil Mohd Atan, Kamel Ariffin Sapar, Siti Hasana Relation between sum of 2mth powers and polynomials of triangular numbers |
| title | Relation between sum of 2mth powers and polynomials of triangular numbers |
| title_full | Relation between sum of 2mth powers and polynomials of triangular numbers |
| title_fullStr | Relation between sum of 2mth powers and polynomials of triangular numbers |
| title_full_unstemmed | Relation between sum of 2mth powers and polynomials of triangular numbers |
| title_short | Relation between sum of 2mth powers and polynomials of triangular numbers |
| title_sort | relation between sum of 2mth powers and polynomials of triangular numbers |
| url | http://psasir.upm.edu.my/id/eprint/35199/ http://psasir.upm.edu.my/id/eprint/35199/ http://psasir.upm.edu.my/id/eprint/35199/1/Relation%20between%20sum%20of%202mth%20powers%20and%20polynomials%20of%20triangular%20numbers.pdf |