Euclide avait-il besoin de l'algorithme d'Euclide pour d\'emontrer l'unicit\'e de la factorisation?

TL;DR

This paper investigates whether Euclid's original work required the Euclidean algorithm to establish the unique factorization property, exploring historical and mathematical perspectives.

Contribution

It provides a historical and mathematical analysis of Euclid's methods, questioning the necessity of the Euclidean algorithm for proving unique factorization.

Findings

Euclid's original proofs may not have relied on the Euclidean algorithm.

Historical analysis suggests alternative methods for proving unique factorization.

The paper clarifies the relationship between Euclid's work and modern algebraic concepts.

Abstract

French translation, by Henri Lombardi and Stefan Neuwirth, of the article "Did Euclid need the Euclidean algorithm to prove unique factorization?", American Mathematical Monthly 113 (2006), pages 196-205.