An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method
Number Theory
2013-10-22 v1
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.
Cite
@article{arxiv.1310.5632,
title = {An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method},
author = {Felix Sidokhine},
journal= {arXiv preprint arXiv:1310.5632},
year = {2013}
}