English

Super-congruences involving trininomial coefficients

Number Theory 2019-10-22 v1

Abstract

The aim of this work is to establish congruences (modp2)\left( \operatorname{mod}p^{2}\right) involving the trinomial coefficients (np1p1)2\binom{np-1}{p-1}_{2} and (np1(p1)/2)2\binom{np-1}{\left( p-1\right)/2}_{2} arising from the expansion of the powers of the polynomial 1+x+x2.1+x+x^{2}. In main results we extend some known congruences involving the binomial coefficients (np1p1)\binom{np-1}{p-1} and (np1(p1)/2)\binom{np-1}{\left( p-1\right) /2} and establish congruences link binomial coefficients and harmonic numbers.

Keywords

Cite

@article{arxiv.1910.09262,
  title  = {Super-congruences involving trininomial coefficients},
  author = {Laid Elkhiri and Miloud Mihoubi},
  journal= {arXiv preprint arXiv:1910.09262},
  year   = {2019}
}
R2 v1 2026-06-23T11:49:38.974Z