On some congruences using multiple harmonic sums of length three and four

Abstract

In the present paper, we determine the sums ${\sum }_{j=1}^{p-1}\frac{H_j^{(s_1)}{H}_j^{(s_3)}}{j^{s_2}}$ and ${\sum }_{j=1}^{p-1}\frac{H_j^{(s_1)}{H}_j^{(s_3)}{H}_j^{(s_4)}}{j^{s_2}}$ modulo $p$ and modulo $p^2$ in certain cases. This is done by using multiple harmonic sums of length three and four, as well as, many other results. In addition, We recover three congruences conjectured by Z.-W Sun and solved later by the author himself and R. Meštrović.

8 pages

Cited by in corpus (1)

• On the Congruence of Finite Generalized Harmonic Numbers Sums Modulo $p^2$