A congruence property of irreducible Laguerre polynomials in two variables

TL;DR

This paper introduces a two-variable irreducible Laguerre polynomial and proves a congruence property analogous to the classical case, expanding understanding of polynomial congruences in multiple variables.

Contribution

It presents a new two-variable irreducible Laguerre polynomial and establishes a congruence property similar to Carlitz's for classical Laguerre polynomials.

Findings

Established a congruence property for the two-variable irreducible Laguerre polynomial.

Extended classical Laguerre polynomial congruences to a multivariable setting.

Provided foundational results for further algebraic and number-theoretic studies.

Abstract

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.