On a kind of generalized multi-harmonic sums
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914177025572864 |
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| author | Wang, Jiaqi Ma, Rong |
| author_facet | Wang, Jiaqi Ma, Rong |
| contents | Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence, which is $$
\sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n$-th Bernoulli number. In this paper, we will generalize this kind of sums and prove a family of similar congruences modulo prime powers $p^r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a kind of generalized multi-harmonic sums Wang, Jiaqi Ma, Rong Number Theory Combinatorics 11B68, 11A07 G.2.1 Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence, which is $$ \sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n$-th Bernoulli number. In this paper, we will generalize this kind of sums and prove a family of similar congruences modulo prime powers $p^r$. |
| title | On a kind of generalized multi-harmonic sums |
| topic | Number Theory Combinatorics 11B68, 11A07 G.2.1 |
| url | https://arxiv.org/abs/2511.23308 |