Related papers: q-Analogue of Wilson's theorem

The Ramanujan--Mordell Theorem for sums of an even number of squares is extended to other quadratic forms and quadratic polynomials.

We study different q-analogues and generalizations of the ex-conjectures of Rodriguez-Villegas. For example, for any odd prime p, we show that the known congruence \sum_{k=0}^{p-1}\frac{{2k\choose k}^2}{16^k} \equiv…

Employing the $q$-Lucas theorem and some known $q$-supercongruences, we give some Dwork-type $q$-congruences, confirming three conjectures in [J. Combin. Theory, Ser. A 178 (2021), Art.~105362]. As conclusions, we obtain the following…

Extending previous work of the author, we compute the Wilson quotient modulo $p^5$ and $p^6$, and equivalently $(p-1)!$ modulo $p^6$ and $p^7$, respectively. Further, we determine some power sums of the Fermat quotients up to modulo $p^6$.…

We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.

In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

In this article we give a proof of a q-analogue of the celebrated four functions theorem. This analogue was conjectured by Bjorner and includes as special cases both the four functions theorem and also Bjorner's q-analogue of the FKG…

We prove some symmetric $q$-congruences.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.

In this paper, the divisibility property of the type 2 $(p, q)$-analogue of the $r$-Whitney numbers of the second kind is established. More precisely, a congruence relation modulo $pq$ for this $(p,q)$-analogue is derived.

Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

In this paper we prove some transformation formulae for congruences modulo a prime and deduce some congruences for Domb numbers and Almkvist-Zudilin numbers. We also pose some conjectures on congruences modulo prime powers.

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

Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors have proven refined results, for example, extending all of…

One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q^f(v) for some linear form f. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials,…

In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a…

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.