On Sums of Practical Numbers and Polygonal Numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910471577141248 |
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| author | Somu, Sai Teja Tran, Duc Van Khanh |
| author_facet | Somu, Sai Teja Tran, Duc Van Khanh |
| contents | Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$. In this paper, we show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two $s$-gonal numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Sums of Practical Numbers and Polygonal Numbers Somu, Sai Teja Tran, Duc Van Khanh Number Theory 11B83, 11D85, 11A99 Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$. In this paper, we show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two $s$-gonal numbers. |
| title | On Sums of Practical Numbers and Polygonal Numbers |
| topic | Number Theory 11B83, 11D85, 11A99 |
| url | https://arxiv.org/abs/2403.13533 |