The p-Adic Valuations of Sums of Binomial Coefficients

In this paper, we prove three supercongruences on sums of binomial coefficients conjectured by Z.-W. Sun. Let p be an odd prime and let h∈ℤ with 2h−1≡0modp. For a∈ℤ+ and pa>3, we show that ∑k=0pa−1hpa−1k2kk−h/2k≡0modpa+1. Also, for any n∈ℤ+, we have νp∑k=0n−1hn−1k2kk−h/2k≥νpn, where νpn denotes t...

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Bibliographic Details
Main Authors: Yong Zhang, Peisen Yuan
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9570350
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