105 citations · 168 across the 35 of their papers we have counts for
6 papers · 1 filter
Some supercongruences arising from symbolic summation
Ji-Cai Liu
Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured b…
On two supercongruences of double binomial sums
Long Li, Ji-Cai Liu
In this note, we confirm two conjectural supercongruences on double sums of binomial coefficients due to El Bachraoui.
Congruence properties for the trinomial coefficients
Moa Apagodu, Ji-Cai Liu
In this paper, we state and prove some congruence properties for the trinomial coeficients, one of which is similar to the Wolstenholme's theorem.
Some congruences related to a congruence of Van Hamme
Victor J. W. Guo, Ji-Cai Liu
We establish some supercongruences related to a supercongruence of Van Hamme, such as \begin{align*} \sum_{k=0}^{(p+1)/2} (-1)^k (4k-1)\frac{(-\frac{1}{2})_k^3}{k!^3} &\equiv p(-1)…
On a congruence involving -Catalan numbers
Ji-Cai Liu
Based on a -congruence of the author and Petrov, we set up a -analogue of Sun--Tauraso's congruence for sums of Catalan numbers, which extends a -congruence due to Tauraso…
Congruences on sums of -binomial coefficients
Ji-Cai Liu, Fedor Petrov
We establish a -analogue of Sun--Zhao's congruence on harmonic sums. Based on this -congruence and a -series identity, we prove a congruence conjecture on sums of central…