Problems and methods at the origin of the theory of numbers

Indice

Preface

Introduction

1. The scene before Fermat
2. Diophantus
3. The Indian mathematicians on Pell equation
4. Leonardo Fibonacci and his contributions to the

theory of numbers

1. Fermat
2. 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