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arXiv:1902.03851 [math.NT]AbstractReferencesReviewsResources

Congruences on sums of $q$-binomial coefficients

Ji-Cai Liu, Fedor Petrov

Published 2019-02-11Version 1

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.

Comments: 11 pages
Categories: math.NT, math.CO
Subjects: 11B65, 11A07, 05A10
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