New congruences on multiple harmonic sums and Bernoulli numbers

摘要

Let P_n denote the set of positive integers which are prime to n. Let B_n be the n-th Bernoulli number. For any prime p > 11 and integer r > 2, we prove that This extends a family of curious congruences. We also obtain other interesting congruences involving multiple harmonic sums and Bernoulli numbers.