In 2016, Deines, Fuselier, Long, Swisher, and Tu proved the following nice supercongruence: \(\begin{aligned} \sum _{k=0}^{p-1}\frac{(\frac{2}{3})_k^3}{k!^3}\equiv -\Gamma _p(\tfrac{1}{3})^3\pmod {p^2}, \end{aligned}\) where \(p\equiv 1\pmod {6}\) is any prime and \(\Gamma _p(x)\) denotes the p-adic Gamma function, and conjectured that this result is also true modulo \(p^3\) . In terms of the q-Dixon formula, the creative microscoping method introduced by Guo and Zudilin (Adv Math 346:329–358, 2019), and the Chinese remainder theorem for coprime polynomials, we shall establish a q-analog of Deines, Fuselier, Long, Swisher, and Tu’s supercongruence for the modulo \(p^3\) case in this paper.
