Factors of certain sums involving central q-binomial coefficients

TL;DR

This paper generalizes and confirms new $q$-congruences involving sums of central $q$-binomial coefficients, expanding on recent results and conjectures in the field.

Contribution

It provides a broader generalization of existing $q$-congruences and verifies additional conjectured identities using established techniques.

Findings

Generalized $q$-congruence proved

Confirmed another conjectured $q$-congruence

Extended the technique to new sums

Abstract

Recently, Ni and Pan proved a $q$-congruence on certain sums involving central $q$-binomial coefficients, which was conjectured by Guo. In this paper, we give a generalization of this $q$-congruence and confirm another $q$-congruence, also conjectured by Guo. Our proof uses Ni and Pan's technique and a simple $q$-congruence observed by Guo and Schlosser.