Related papers: Some symmetric $q$-congruences

We prove several congruences for trinomial coefficients.

We establish a q-analogue of Wolstenholme's harmonic series congruence.

In this paper we establish a $q$-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.

We prove an interesting symmetric $q$-series identity which generalizes a result due to Ramanujan. A proof that is analytic in nature is offered, and a bijective-type proof is also outlined.

We prove a necessary and sufficient condition for a symmetric association scheme to be a Q-polynomial scheme.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.

We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.

We show some new Wolstenholme type $q$-congruences for some classes of multiple $q$-harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most of these results are $q$-extensions of the corresponding…

We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by…

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

We prove a Lucas-type congruence for q-Delannoy numbers.

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun--Tauraso's congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.

In this paper we present many congruences for several Ap\'ery-like sequences.