A Note on the Number of Representations of $n$ as a Sum of Generalized Polygonal Numbers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912013573160960 |
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| author | Bandyopadhyay, Subhajit Baruah, Nayandeep Deka |
| author_facet | Bandyopadhyay, Subhajit Baruah, Nayandeep Deka |
| contents | Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result that gives such relations for $s$-gonal numbers for any integer $s\geq3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on the Number of Representations of $n$ as a Sum of Generalized Polygonal Numbers Bandyopadhyay, Subhajit Baruah, Nayandeep Deka Number Theory Combinatorics 05A17 (Primary) 11P81, 11P83, 11B37 (Secondary) Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result that gives such relations for $s$-gonal numbers for any integer $s\geq3$. |
| title | A Note on the Number of Representations of $n$ as a Sum of Generalized Polygonal Numbers |
| topic | Number Theory Combinatorics 05A17 (Primary) 11P81, 11P83, 11B37 (Secondary) |
| url | https://arxiv.org/abs/2409.02023 |