Related papers: A generalization of Carlitz's congruence

In the paper, we generalize some congruences of Lehmer for general composite numbers.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

In this article we discuss a generalized Wirtinger inequality.

We generalize the concept of disjunction.

In the present note a generalization of Borel-Cantelli Lemma is proposed.

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

In this paper we give a generalization of a result of Wei.

We give a generalization of Wolstenholme's harmonic series congruence for the Lucas sequences.

This paper presents a new formula for the q-shift operator, building on the techniques by Liu and Sears. This formula provides fresh proof of the Carlitz formula and extends it naturally. As applications, we derive an equivalent form of the…

Carlitz proved a few generalizations of Mehler's formula. Later, Srivastava et al. gave a new proof for some extensions of Carlitz's formula. Here, a direct proof of the further generalization is given.

A generalization of the law of total covariance is presented and proved.

A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.

One of the variants to proof the generalized Ito-Wentzell's formula is introduced and examined in this paper. The relationship between different representations of the generalized Ito-Wentzell's formula/ is considered.

In this paper we introduce a version of irreducible Laguerre polynomials in two variables and prove for it a congruence property, which is similar to the one obtained by Carlitz for the classical Laguerre polynomials in one variable.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

We prove several congruences for trinomial coefficients.

In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…

In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.