# On a congruence involving $q$-Catalan numbers

## TL;DR

This paper develops a $q$-analogue of a known congruence involving sums of Catalan numbers, extending previous results and based on a specific $q$-congruence established by the author and Petrov.

## Contribution

The paper introduces a new $q$-analogue of Sun--Tauraso's congruence for Catalan number sums, expanding the scope of $q$-congruence theory.

## Key findings

- Established a $q$-analogue of Sun--Tauraso's congruence
- Extended Tauraso's $q$-congruence results
- Connected $q$-congruences with classical Catalan number properties

## Abstract

Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun--Tauraso's congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.