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

Claus-Peter Wirth
2010 arXiv   pre-print
We present the only proof of Pierre Fermat by descente infinie that is known to exist today.  ...  Including all important facts, we present a concise and self-contained discussion of Fermat's proof sketch, which is easily accessible to laymen in number theory as well as to laymen in the history of  ...  Acknowledgements I would like to thank Paolo Bussotti for a list of suggestions for improvement on an earlier version of this paper, for some profound help, and for much more.  ... 
arXiv:0902.3623v4 fatcat:2nce5esnfzgbrdw5opkykh4f5e

Automation of Mathematical Induction as part of the History of Logic [article]

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
We review the history of the automation of mathematical induction  ...  Descente Infinie The soundness of the induction method of § 4.6 is most easily seen when the argument is structured as a proof by contradiction, assuming a counterexample.  ...  For Fermat's historic reinvention of the method, it is thus just natural that he developed the method in terms of assumed counterexamples. 57 Here is Fermat's Method of Descente Infinie in modern language  ... 
arXiv:1309.6226v5 fatcat:i7nzngq47zfd7its4kfynlfpti

A Simplified and Improved Free-Variable Framework for Hilbert's epsilon as an Operator of Indefinite Committed Choice [article]

Claus-Peter Wirth
2017 arXiv   pre-print
The quantificational expressiveness and the problem-solving facilities of our framework exceed standard first-order and even higher-order modal logics, and directly support Fermat's descente infinie.  ...  We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only two kinds of free variables left (instead of three): implicitly universally  ...  Note, however, that [ Wirth, 2004 ] additionally contains some comparative discussions and compatible extensions for descente infinie, which also apply to our new version here.  ... 
arXiv:1104.2444v9 fatcat:z4d4xpltd5ggpnriisvu37svfu

Leonhard Euler: The First St. Petersburg Years (1727–1741)

Ronald Calinger
1996 Historia Mathematica  
ACKNOWLEDGMENTS A portion of this paper was first presented at the conference in honor of Allen G. Debus held at the University of Chicago on October 30, 1991.  ...  David Wilt of the Engineering-Mathematics Library at the University of Maryland, College Park, for making Euler's Opera accessible.  ...  It examined Frenicle de Bessy's proof for n ϭ 4 and Fermat's method of infinite descent [38] . He read of these in Fermat's notes on Diophantus's Arithmetica. B.  ... 
doi:10.1006/hmat.1996.0015 fatcat:oegvzestu5bctbsf5mxy42vpwq

Looking backward: From Euler to Riemann [article]

Athanase Papadopoulos
2017 arXiv   pre-print
The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration,  ...  and the notion of space.  ...  with a sketch of a proof. The result became known as the "prime number theorem."  ... 
arXiv:1710.03982v1 fatcat:vnre7wfvybcalafm2hcq5adpji

Looking Backward: From Euler to Riemann [chapter]

Athanase Papadopoulos
2017 From Riemann to Differential Geometry and Relativity  
with a sketch of a proof. The result became known as the "prime number theorem."  ...  known that the Greeks had a method to list effectively the sequence of primes (Eratosthenes sieve).  ... 
doi:10.1007/978-3-319-60039-0_1 fatcat:va7zb3jsprejvbrvbvpacqgp2q

Diophantus of Alexandria : a Text and its History

Norbert Schappacher
2005 unpublished
It was first proved by Fermat with his technique of descent (descente infinie). 51 The Arab number theorists have opened up mathematics for this kind of The proof is sketched, and constitutes the only  ...  explicit sketch by Fermat of a proof problem.  ...