A q-ANALOGUE OF A HYPERGEOMETRIC CONGRUENCE. Issue 2 (18th April 2020) - GU, CHENG-YANG; GUO, VICTOR J. W.
Abstract : We give a q -analogue of the following congruence: for any odd prime p, eqnarray_k=0^(p-1)/2(-1)^k(6k+1)(12)_k^3k!^38^k_j=1^k(1(2j-1)^2-116j^2)0 (mod p), eqnarray which was originally conjectured by Long and later proved by Swisher. This confirms a conjecture of the second author ['A q -analogue of the (L.2) supercongruence of Van Hamme', J. Math. Anal. Appl. 466 (2018), 749–761].