On congruences related to trinomial coefficients and harmonic numbers

Authors

NEŞE ÖMÜR
SİBEL KOPARAL
LAID ELKHIRI

Abstract

In this paper, we establish some congruences involving the trinomial coefficients and harmonic numbers. For example, for any prime $p>3,$ \begin{equation*} \sum\limits_{k=0}^{p-1}\left( -1\right) ^{k}\binom{p-1}{k}_{2}H_{k}\equiv 0 \ \pmod {p}. \end{equation*}

DOI

10.3906/mat-2101-128

Keywords

Congruences, binomial coefficients, trinomial coefficients, harmonic numbers

First Page

1592

Last Page

1604

Recommended Citation

ÖMÜR, NEŞE; KOPARAL, SİBEL; and ELKHIRI, LAID (2021) "On congruences related to trinomial coefficients and harmonic numbers," Turkish Journal of Mathematics: Vol. 45: No. 4, Article 8. https://doi.org/10.3906/mat-2101-128
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/8