## From Fermat to Gauss: indefinite descent and methods of reduction in number theory |

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### Contents

Introduction 116 | 1 |

Indefinite descent and complete induction 1213 | 12 |

Fermat and the indefinite descent 31176 | 31 |

Copyright | |

24 other sections not shown

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### Common terms and phrases

algorithm analyse applied argument arithmetic arithmeticae binary quadratic forms Brouncker complete induction concept connected continued fractions convergents coprime cube deduce demonstration by descent Diophantus Disquisitiones Disquisitiones arithmeticae divided divisors elementary equation x2 equivalent Euler Euler's demonstration example exists exposed fact factor Fermat wrote Fermat's great theorem form 4n+l form 8n+3 form x2 four squares theorem Frenicle Furthermore Gauss hence hypothesis Ibidem identity important indefinite descent infinite number initial segment integer numbers integer solutions integer squares Lagrange Lagrange's let us consider let us suppose letter to Huygens logical mathematical mathematicians methodological mutually prime squares natural numbers necessary negative nombre number theory numeris obtained odd number Paolini's demonstration Paragraph Pell's equation posed possible prime number problem proof proposition Pythagorean triangle quadratic residues reasoning reductio ad absurdum reduction-descent smaller smallest solving sum of distinctions sum of four sum of three term theorem concerning three squares triangular numbers underline Wallis