相关论文: On an identity of Sylvester

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

Sylvester's identity is a classical determinantal identity with a straightforward linear algebra proof. We present a new, combinatorial proof of the identity, prove several non-commutative versions, and find a $\beta$-extension that is both…

We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

In this paper we deal with the noteworthy Sylvester's determinantal identity and some of its generalizations. We report the formulae due to Yakovlev, to Gasca, Lopez--Carmona, Ramirez, to Beckermann, Gasca, M\"uhlbach, and to Mulders in a…

In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…

In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…

The aim of this paper is to present a general algebraic identity. Applying this identity, we provide several formulas involving the q-binomial coefficients and the q-harmonic numbers. We also recover some known identities including an…

A family of general integral identities is derived and several applications of physical interest are presented

In this article we shows some results about algebra with the group of units having special polynomial identity.

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.

We exhibit an identity that plays the same role as Vaughan's identity but is arguably simpler

We show how the Fibonacci's identity is used to obtain Euler bricks. Also,we put forward the relation between Fibonacci's identity and Euler's formula, which provides the description of Euler's bricks with noninteger spatial diagonal.…

We investigate extensions of Malcev algebras and give an explicit example of extended algebras. We present a new algebraic identity, which can be regarded as a generalization of the Jacobi identity or the Malcev identity. As applications to…

We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…

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…

Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

In this short note we provide some algebraic identity with a proof exploiting its probabilistic interpretation. We show several consequences of the identity, in particular we obtain a new representation of a Stirling number of second kind,…