A q-supercongruence modulo the fourth power of a cyclotomic polynomial
Abstract
In this paper, a new q-supercongruence with two free parameters modulo the fourth power of a cyclotomic polynomial is obtained. Our main auxiliary tools are Watson's 8φ7 transformation formula for basic hypergeometric series, the `creative microscoping' method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials. By taking suitable parameter substitutions in the established q-supercongruence, some nice congruences involving the Bernoulli numbers are derived.
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