Séminaire Lotharingien de Combinatoire, B63g (2010), 8 pp.

Roberto Tauraso

New Harmonic Number Identities with Applications

Abstract. We determine the explicit formulas for the sum of products of homogeneous multip le 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 pr ime.

Received: February 3, 2010. Accepted: June 11, 2010.

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