Author(s)

Zhongyan Shen¹, Tianxin Cai²

¹Department of Mathematics, Zhejiang International Studies University, Hangzhou, China.
²Department of Mathematics, Zhejiang University, Hangzhou, China.

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 P_P 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.

Bernoulli Numbers, Alternating Harmonic Sums, Congruences, Modulo Prime Powers

Shen, Z. and Cai, T. (2020) Super Congruences Involving Alternating Harmonic Sums. Advances in Pure Mathematics, 10, 611-622. doi: 10.4236/apm.2020.1010037.