Some Families of Super Congruences Involving Alternating Multiple Harmonic Sums
| Autor: | Jerry Qu, Kevin Chen, David Wang, Rachael Hong, Jianqiang Zhao |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Combinatorics Mathematics - Number Theory Mathematics::Number Theory 010102 general mathematics Harmonic (mathematics) 010103 numerical & computational mathematics 01 natural sciences FOS: Mathematics Condensed Matter::Strongly Correlated Electrons Number Theory (math.NT) 11A07 11B68 0101 mathematics Mathematics |
| Popis: | Let $p$ be a prime. In this short note we study some families of super congruences involving the following alternating sums \begin{equation*} \sum_{\substack{j_1+j_2+\cdots+j_n=2 p^r p\nmid j_1 j_2 \cdots j_n}} \frac{(-1)^{j_1+\cdots+j_b}}{j_1\cdots j_n} \pmod{p^r}, \end{equation*} which extend similar statements proved by Shen and Cai who treated the cases when $n=4,5$. 10 pages, Acta Arithmetica, 2018 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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