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which was originally conjectured by Long and later proved by Swisher. This confirms a conjecture of the second author [‘A
-analogue of the (L.2) supercongruence of Van Hamme’, J. Math. Anal. Appl.466 (2018), 749–761].
We prove some congruences on sums involving fourth powers of central q-binomial coefficients. As a conclusion, we confirm the following supercongruence observed by Long [Pacific J. Math. 249 (2011), 405–418]: