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, N, KOPARAL, S, & ELKHIRI, L (2021). On congruences related to trinomial coefficients and harmonic numbers. Turkish Journal of Mathematics 45 (4): 1592-1604. https://doi.org/10.3906/mat-2101-128

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