TITLE:
Super Congruences Involving Alternating Harmonic Sums
AUTHORS:
Zhongyan Shen, Tianxin Cai
KEYWORDS:
Bernoulli Numbers, Alternating Harmonic Sums, Congruences, Modulo Prime Powers
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.10,
October
29,
2020
ABSTRACT: Let p be an odd prime, the harmonic congruence such as , and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, where PP denotes the set of positive integers which are prime to p. And we establish the combinational congruences involving alternating harmonic sums for positive integer n=3,4,5.