A Self-Contained and Easily Accessible Discussion of the Method of Descente Infinie and Fermat's Only Explicitly Known Proof by Descente Infinie

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SEKI Working-Paper SWP-2006-02
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SEKI

Abstract

We present the only proof of Pierre Fermat by descente infinie that is known to exist today. We discuss descente infinie from the mathematical, logical, historical, linguistic, and refined logic-historical points of view. We provide the required preliminaries from number theory and present a self-contained proof in a modern form, which nevertheless is intended to follow Fermat's ideas as interpreted into the cited Latin original. We then annotate an English translation of Fermat's original proof with terms from the modern proof. Although the paper consists of reviews, compilations, and simple number theory with mainly pedagogical intentions, its gestalt is original and it fills a gap regarding the easy accessibility of the subject.

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by Paolo Bussotti

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