A systematic approach to Diophantine equations: two thousand solved examples

TL;DR

This paper provides a comprehensive collection of complete solutions to 2000 Diophantine equations of varying difficulty, serving as a valuable database for researchers and students working on polynomial Diophantine problems.

Contribution

It offers the first complete solutions to a large set of Diophantine equations, systematically organized and accessible for further research and problem reduction.

Findings

Complete solutions to 2000 Diophantine equations provided

Organized summary table of equations by size included

Database facilitates reduction of complex equations to known solutions

Abstract

Monograph "B. Grechuk, Polynomial Diophantine equations. A systematic approach" suggests solving Diophantine equations systematically in certain order. Many hundreds of the equations are left to the reader. Here, we provide complete solutions to all these equations. The difficulties of solved equations range from elementary to research level. In the last section, we present a summary table of all solved equations ordered by their size, which makes them easy to find. As a result, this document may be used as a database of solved Diophantine equations of small size, to which more difficult equations can be reduced.