Abstract

Let be the nth Euler number and the rising factorial. Let p>3 be a prime. In 2012, Sun proved that which is a refinement of a famous supercongruence of Van Hamme. In 2016, Chen, Xie, and He established the following result: which was originally conjectured by Sun. In this paper, we give q-analogues of the above two supercongruences as well as another supercongruence related to Euler numbers by employing the q-WZ method. As a conclusion, we also provide a q-analogue of the following supercongruence of Sun:

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