| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4593299 | Journal of Number Theory | 2016 | 11 Pages |
Abstract
The Delannoy numbers and Schröder numbers are given byDn=∑k=0n(nk)(n+kk)andSn=∑k=0n(nk)(n+kk)1k+1, respectively. Let p>3p>3 be a prime. We mainly prove that∑k=1p−1DkSk≡2p3Bp−3−2pHp−1⁎(modp4), where BnBn is the n -th Bernoulli number and these Hn⁎ are the alternating harmonic numbers given by Hn⁎=∑k=1n(−1)kk. This supercongruence was originally conjectured by Z.-W. Sun in 2011.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ji-Cai Liu,