An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method

Felix Sidokhine

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arXiv · 1310.5632

An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method

Felix Sidokhine

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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.

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Felix Sidokhine. 2013-10-21. An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method. https://arxiv.org/abs/1310.5632

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