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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9570350 |
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