Paolo Bussotti
Editore: Officine Grafiche Francesco Giannini & Figli S.p.A
Anno: 2007
Collana: Quaderni dell'Accademia Pontaniana
Pagine: 136
Legatura: Brossura
ISBN: 9009054

testo in inglese

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CONTENT

Preface

Introduction

I. The scene before Fermat

1. Diophantus

2. The Indian mathematicians on Pell equation

3. Leonardo Fibonacci and his contributions to the

theory of numbers

II. Fermat

1. The birth of modern number theory:

the basic ideas and the problems

2. The demonstrations of the theorems enunciated by Fermat

2.1. Brief history of these demonstrations

2.2. The indefinite descent

2.2.a. What the indefinite descent is

2.2. b. There is no Pythagorean triangle whose area is equal

to the square of an integer number

2.2.c. Every prime of the form 4n+1 is the sum of two squares

2.2.d. Every integer is the sum of three triangular numbers

2.2.e. The four squares theorem

3. The interconnections between the theorems by Fermat and

his conception of arithmetic

III. Conclusions

Bibliography

Content