On the Modern Structure of the Gauss-Landau Theorem

TL;DR

This paper formalizes the Gauss-Landau theorem, offering a unified approach to computing GCD and LCM of integer sets, aiming to improve understanding and application in mathematics education and research.

Contribution

It introduces a formalized, named version of the Gauss-Landau theorem with a unified prime factorization approach, filling a gap in the literature.

Findings

Provides a formal proof of the Gauss-Landau theorem

Unifies GCD and LCM computations through prime factorization

Enhances mathematical understanding and teaching methods

Abstract

We formalize the Gauss-Landau theorem, providing a unified prime factorization approach to computing the GCD and LCM of finite nonzero integer sets. Although commonly used as a heuristic or technique in elementary number theory education, these theorems have not been explicitly formalized or named in the literature. This formalization aims to enhance understanding and facilitate adoption in mathematical instruction and research.