Super-congruences involving trininomial coefficients

2019/10/21 by Laid Elkhiri, Elkhiri, Laid, Miloud Mihoubi +1
Mathematics · Physics and Astronomy · #05A10 #11A07 #11B65 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.09262

openalex publication_date 2019/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to establish congruences ( modp²) involving the trinomial coefficients \binomnp-1p-1₂ and \binomnp-1( p-1)/2₂ arising from the expansion of the powers of the polynomial 1+x+x². In main results we extend some known congruences involving the binomial coefficients \binomnp-1p-1 and \binomnp-1( p-1) /2 and establish congruences link binomial coefficients and harmonic numbers.

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