English

Some Congruences Involving Binomial Coefficient and Fermat Quotient

Number Theory 2025-12-02 v1

Abstract

In this paper, we investigate some congruences involving sums of dk(xk)(x+kk)(2kk)\frac{d^{-k}{x\choose k}{x+k\choose k}}{{2k \choose k}}, where xx be a pp-adic integer, kk be a non-negative integer, and dd (d0)(d\neq 0) be a rational number.

Keywords

Cite

@article{arxiv.2512.01385,
  title  = {Some Congruences Involving Binomial Coefficient and Fermat Quotient},
  author = {Wei-Wei Qi},
  journal= {arXiv preprint arXiv:2512.01385},
  year   = {2025}
}
R2 v1 2026-07-01T08:03:13.249Z