Related papers: On AZ-style identity
Menon's identity is $\sum_{a \in A}^m (a-1,m) = d(m) \varphi(m)$, where $A$ is a reduced set of residues modulo $m$. This paper contains elementary proofs of some generalizations of this result.
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
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.
A generalization of an inequality from IMO is proven.
In this paper, we propose a generalization of a congruence due to Carlitz.
In this article we discuss a generalized Wirtinger inequality.
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…
We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main…
We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character,…
A family of general integral identities is derived and several applications of physical interest are presented
In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.
An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that…
An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to…
A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.
In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary.
A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Hall-Littlewood, Jack and Macdonald polynomials. We also give a simple proof of…
We give axiomatic characterisations of generalized $\psi$-estimators and (usual) $\psi$-estimators (also called $Z$-estimators), respectively. The key properties of estimators that come into play in the characterisation theorems are the…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In this paper, based on the WZ theory, a very succinct new proof, of an identity by Chaundy and Bullard, was given.