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-Supercongruences on triple and quadruple sums
Xiaoxia Wang, Chang Xu
Inspired by the recent work of El Bachraoui, we present some new -supercongruences on triple and quadruple sums of basic hypergeometric series. In particular, we give a -supe…
Some new results about -trinomial coefficients
Yifan Chen, Chang Xu, Xiaoxia Wang
In this paper, we present several new congruences on the -trinomial coefficients introduced by Andrews and Baxter. A new congruence on sums of central -binomial coefficients…
New q-supercongruences from the Bailey transformation
Xiaoxia Wang, Chang Xu
Inspired by the recent work of Guo, we establish some new q-supercongruences including q-analogues of some Ramannujan-type supercongruences, by using the Bailey transformation form…
A -supercongruence modulo the fourth power of a cyclotomic polynomial
Xiaoxia Wang, Chang Xu
In this paper, a new -supercongruence with two free parameters modulo the fourth power of a cyclotomic polynomial is obtained. Our main auxiliary tools are Watson's tran…
Some q-supercongruences on double and triple sums
Xiaoxia Wang, Chang Xu
In this paper, we investigate a number of -supercongruences on double and triple sums. By means of a lemma devised by El Bachraoui and its generalization, we transform some -…