Published 2019-07-15
Keywords
- harmonic numbers,
- Euler number,
- congruences
Copyright (c) 2024 Scientia Series A: Mathematical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
A congruence for a double harmonic sum. (2019). Scientia Series A: Mathematical Sciences, 29, 37-44. https://revistas.usm.cl/scientia/article/view/38
Abstract
In this short note, our primary purpose is to prove the congruence
\[\sum_{k=1}^{\frac{p-1}{2}} \frac{(-1)^k}{k} \sum_{j=\lfloor\frac{k}{2}\rfloor+1}^{k} \frac{1}{2j-1} \equiv 0 \mod p\]
Along the way, a number of auxiliary results of independent interest are found.
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