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

TL;DR

This paper explores congruence properties of finite generalized harmonic number sums modulo p^2, introducing a simplified analytical method and presenting new results for specific cases.

Contribution

It offers a more transparent method for analyzing harmonic sums modulo p^2 and extends known results with new findings for special cases.

Findings

New congruence relationships for harmonic sums modulo p^2

Simplified analytical approach for these sums

Additional results for specific cases

Abstract

In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special cases.