Diophantine m-tuples

The problem of the construction of Diophantine m-tuples, i.e. sets with the property that product of any two of its distinct elements is one less then a square, has a very long history. There are some new results in this area, but many open problems and unproved conjectures still remains. In this survey we explain the main problems and results concerning Diophantine m-tuples.

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Andrej Dujella

Table of contents

1. Introduction

2. Diophantine quintuple conjecture

3. Sets with the property D(n)

4. Connections with Fibonacci numbers

5. Rational Diophantine m-tuples

6. Connections with elliptic curves

7. Various generalizations

8. References (543 titles)