Super-congruences involving trininomial coefficients

Laid Elkhiri; Miloud Mihoubi

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arXiv · 1910.09262

Super-congruences involving trininomial coefficients

Laid Elkhiri·Miloud Mihoubi

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Abstract

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

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Laid Elkhiri, Miloud Mihoubi. 2019-10-21. Super-congruences involving trininomial coefficients. https://arxiv.org/abs/1910.09262

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