Modulus p² congruences involving harmonic numbers

2018/03/08 by Yang, Jizhen, Wang, Yunpeng
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.02966

Abstract

The harmonic number H_k=∑_j=1^k1/j(k=1,2,3⋯) play an important role in mathematics. Let p>3 be a prime. In this paper, we establish a number of congruences with the form ∑_k=1^p-1k^mH_kⁿ(\mod p²) for m=1,2⋯,p-2 and n=1,2,3.

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