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A family of super congruences involving multiple harmonic sums

2016/04/07 by Megan McCoy, Kevin Thielen, Liuquan Wang +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Congruence (geometry) #Congruence relation #Coprime integers #Harmonic #Modulo #Prime (order theory) #math.NT #msc:11A07 #msc:11B68

paper · pdf · doi:10.1142/s1793042117500075

published as International J. Number Theory, Vol. 13, No. 1 (2017) 109-128 · 16 pages, final version for publication

openalex publication_date 2016/04/07 · openalex created_date 2016/06/24 · arxiv created 2021/01/21 · arxiv updated 2021/01/22 · openalex updated_date 2026/08/06

Abstract

In recent years, the congruence [Formula: see text] first discovered by the last author has been generalized by either increasing the number of indices and considering the corresponding super congruences, or by considering the alternating version of multiple harmonic sums. In this paper, we prove a family of similar super congruences modulo prime powers [Formula: see text] with the indices summing up to [Formula: see text] where [Formula: see text] is coprime to [Formula: see text], and where all the indices are also coprime to [Formula: see text].

Citations