New harmonic number identities with applications

Details New harmonic number identities with applications New harmonic number identities with applications

2009-12-13

arxiv.org/abs/0912.2497v1

Mathematics

Number Theory

Scientific paper

We determine the explicit formulas for the sum of products of homogeneous
multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when
$\sum_{j=1}^r \lambda_j\leq 5$. We apply these identities to the study of two
congruences modulo a power of a prime.

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