Modulus p^2 congruences involving harmonic numbers

Abstract

The harmonic number $H_k={\sum }_{j=1}^{k}1/j(k=1,2,3\cdots )$ play an important role in mathematics. Let $p>3$ be a prime. In this paper, we establish a number of congruences with the form ${\sum }_{k=1}^{p-1}{k}^m{H}_k^n(\mathrm{mod}{p}^2)$ for $m=1,2\cdots ,p-2$ and $n=1,2,3$.

References in corpus (1)

• Quasi-symmetric functions and mod p multiple harmonic sums