Congruences on sums of $q$-binomial coefficients

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.

11 pages

References in corpus (2)

• Congruences for $q$-binomial coefficients
• Some new $q$-congruences for truncated basic hypergeometric series: even powers

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