Year: 2013
Type: preprint
Abstract: The goal of this notice is to present a proof of Bachet's conjecture based exclusively on the fundamental theorem of arithmetic. The novelty of this proof consists in its introduction of a partial order on rational integers through the unique factorization property. In general, the proofs of Bachet's conjecture by Lagrange - Euler's method assume necessary the use of infinite descent. In the proposed proof we do not assume the existence of a "minimal solution", but rather we show the existence of the desired solution through an algorithmic method.
Source: arXiv (Cornell University)
Author: Sidokhine, Felix
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1815386911