  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.
