English

On some conjectural congruences

Number Theory 2020-06-30 v1 Combinatorics

Abstract

In this paper, we confirm some congruences conjectured by V.J.W. Guo and M.J. Schlosser recently. For example, we show that for primes p>3p>3, k=0p1(2pk2k1)(1p1)k2p2(k!)2p20(modp5). \sum_{k=0}^{p-1}(2pk-2k-1)\frac{\left(\frac{-1}{p-1}\right)_k^{2p-2}}{(k!)^{2p-2}}\equiv0\pmod{p^5}.

Keywords

Cite

@article{arxiv.1904.02550,
  title  = {On some conjectural congruences},
  author = {Chen Wang},
  journal= {arXiv preprint arXiv:1904.02550},
  year   = {2020}
}

Comments

8 pages

R2 v1 2026-06-23T08:29:18.985Z