On a kind of generilized multi-harmonic sum
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914176455147520 |
|---|---|
| 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 $$
\sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n-$th Bernoulli numbers. In this paper, we will generalize this problem by using congruent theory and combinatorial methods, and we get some curious congruences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a kind of generilized multi-harmonic sum Wang, Jiaqi Ma, Rong Number Theory Combinatorics Primary 11B68, Secondary 11A07 Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence $$ \sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n-$th Bernoulli numbers. In this paper, we will generalize this problem by using congruent theory and combinatorial methods, and we get some curious congruences. |
| title | On a kind of generilized multi-harmonic sum |
| topic | Number Theory Combinatorics Primary 11B68, Secondary 11A07 |
| url | https://arxiv.org/abs/2411.03148 |