Three pairs of congruences concerning sums of central binomial coefficients

Author:

Mao Guo-Shuai1,Tauraso Roberto2ORCID

Affiliation:

1. Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy

Abstract

Recently the first author proved a congruence proposed in 2006 by Adamchuk: [Formula: see text] for any prime [Formula: see text]. In this paper, we provide more examples (with proofs) of congruences of the same kind [Formula: see text] where [Formula: see text] is a prime such that [Formula: see text], [Formula: see text] is a fraction in [Formula: see text] and [Formula: see text] is a [Formula: see text]-adic integer. The key ingredients are the [Formula: see text]-adic Gamma function [Formula: see text] and a special class of computer-discovered hypergeometric identities.

Funder

Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. ON GUILLERA’S -SERIES FOR;Bulletin of the Australian Mathematical Society;2023-02-09

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