### „Ich habe hierfür einen wahrhaft wunderbaren Beweis, doch ist dieser Rand hier zu schmal, um ihn zu fassen.“

— Pierre de Fermat

Randnotiz von 1637, die Generation von Mathematikern beschäftigte, s. w:Großer fermatscher Satz#Ursprung.

1 0## Pierre de Fermat

**Geburtstag:** 17. August 1601**Todesdatum:** 12. Januar 1665

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Pierre de Fermat [pjɛːʀ dəfɛʀˈma] war ein französischer Mathematiker und Jurist.

— Pierre de Fermat

Randnotiz von 1637, die Generation von Mathematikern beschäftigte, s. w:Großer fermatscher Satz#Ursprung.

— Pierre de Fermat

Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.
Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, [http://books.google.com/books?id=L6QKAAAAYAAJ The Pell Equation] (1912)

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— Pierre de Fermat

Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.
Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, [http://books.google.com/books?id=L6QKAAAAYAAJ The Pell Equation] (1912)

— Pierre de Fermat

Fermat (in a letter dated October 18, 1640 to his friend and confidant Frénicle de Bessy) commenting on his statement<!--Fermat's statement--> that p divides a<sup> p−1</sup> − 1 whenever p is prime and a is coprime to p (this is what is now known as Fermat's little theorem).

— Pierre de Fermat

Note written on the margins of his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, this was taken as an indication of what became known as Fermat's last theorem, a correct proof for which would be found only 357 years later; as quoted in Number Theory in Science and Communication (1997) by Manfred Robert Schroeder

— Pierre de Fermat

Epist. XLII, written at Toulouse (Jan. 1, 1662) and reprinted in Œvres de Fermat, ii, p. 457; i, pp. 170, 173, as quoted by , A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century (1910) [https://books.google.com/books?id=CGJDAAAAIAAJ&pg=PA10 p. 10.]