On congruences related to trinomial coefficients and harmonic numbers

Authors

NEŞE ÖMÜR
SİBEL KOPARAL
LAID ELKHIRI

DOI

10.3906/mat-2101-128

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*}

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