On a kind of generilized multi-harmonic sum

2024/11/05 by Wang, Jiaqi, Ma, Rong · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11B68 #Secondary 11A07

paper · doi:10.48550/arxiv.2411.03148

Abstract

Let p be an odd prime, Jianqiang Zhao has established a curious congruence ∑_{i+j+k=p \atop i,j,k gt; 0} (1)/(ijk) ≡ -2B_p-3\pmod p , where B_n denotes the n-th Bernoulli numbers. In this paper, we will generalize this problem by using congruent theory and combinatorial methods, and we get some curious congruences.

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