Theoretical derivation demonstrates unified q-analogues of Van Hamme supercongruences, highlighting new algebraic connections to Bernoulli numbers.
Applying the q-Zeilberger algorithm, we establish a unified q-analogue of the (C.2) and (G.2) supercongruences of Van Hamme, which can be viewed as a refinement of several previously known results. As consequences, we obtain a q-analogue of supercongruence involving Bernoulli numbers, as well as a refinement of (G.2) supercongruence.
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Li et al. (2026) studied this question.
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