Congruences on sums of $q$-binomial coefficients

Ji-Cai Liu; Fedor Petrov

doi:10.1016/j.aam.2020.102003

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arXiv · 1902.03851

Congruences on sums of $q$-binomial coefficients

Ji-Cai Liu·Fedor Petrov

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Abstract

We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu and Zeilberger from Guo's $q$-congruence.

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Ji-Cai Liu, Fedor Petrov. 2019-02-11. Congruences on sums of $q$-binomial coefficients. https://doi.org/10.1016/j.aam.2020.102003

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