Arithmetic theory of harmonic numbers (II)

Abstract

For $k=1,2,\ldots$ let $H_k$ denote the harmonic number $\sum_{j=1}^k 1/j$. In this paper we establish some new congruences involving harmonic numbers. For example, we show that for any prime $p>3$ we have $$\def\f#1#2{\frac{#1}{#2}}\sum_{k=1}^{p-1}\f{H_k