2 citations · 3 across the 14 of their papers we have counts for
21 papers
On the divisibility of sums of even powers of -binomial coefficients
Ji-Cai Liu, Xue-Ting Jiang
We prove the divisibility conjecture on sums of even powers of -binomial coefficients, which was recently proposed by Guo, Schlosser and Zudilin. Our proof relies on two -har…
On the divisibility of -trinomial coefficients
Ji-Cai Liu
We establish a congruence on sums of central -binomial coefficients. From this -congruence, we derive the divisibility of the -trinomial coefficients introduced by Andrews…
An extension of a supercongruence of Long and Ramakrishna
Victor J. W. Guo, Ji-Cai Liu, Michael J. Schlosser
We prove two supercongruences for specific truncated hypergeometric series. These include an uniparametric extension of a supercongruence that was recently established by Long and…
A -adic analogue of Chan and Verrill's formula for
Ji-Cai Liu
We prove three supercongruences for sums of Almkvist-Zudilin numbers, which confirm some conjectures of Zudilin and Z.-H. Sun. A typical example is the Ramanujan-type supercongruen…
Supercongruences for sums involving Domb numbers
Ji-Cai Liu
We prove some supercongruence and divisibility results on sums involving Domb numbers, which confirm four conjectures of Z.-W. Sun and Z.-H. Sun. For instance, by using a transform…
Supercongruences for Almkvist--Zudilin sequences
Ji-Cai Liu, He-Xia Ni
In this note, we prove two supercongruences involving Almkvist--Zudilin sequences, which were originally conjectured by Z.-H. Sun.