A Generalization of Diophantine Tuples

TL;DR

This paper extends the concept of Diophantine tuples to finite fields, using advanced methods to derive results that improve the understanding of their distribution and quantity.

Contribution

It generalizes Diophantine tuples to finite fields and applies Shparlinski's method to achieve power-saving bounds on their count.

Findings

Derived power-saving estimates for the number of generalized Diophantine tuples

Extended classical Diophantine tuple concepts to finite fields

Provided new bounds improving previous results

Abstract

This paper investigates a generalized version of Diophantine tuples in finite fields. Applying Shparlinski's method, we obtain power-saving results on the number of such tuples.