Arithmetic-term representations for the greatest common divisor

TL;DR

This paper introduces novel arithmetic-term representations for the gcd function, including a modular term approach, enhancing the understanding and computation of gcd in integer arithmetic.

Contribution

The paper presents new arithmetic-term representations for gcd, including a modular term-based method, advancing theoretical understanding and potential computational applications.

Findings

New arithmetic-term representation for gcd

Representation using modular terms in integer arithmetic

Enhanced theoretical framework for gcd computation

Abstract

We construct a new arithmetic-term representation for the function gcd(a,b). As a byproduct, we also deduce a representation gcd(a,b) by a modular term in integer arithmetic.